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Objectives The purpose of our study was to describe children with life-threatening bleeding. Design We conducted a prospective observational study of children with life-threatening bleeding events. Setting Twenty-four childrens hospitals in the United States, Canada, and Italy participated. Subjects Children 0-17 years old who received greater than 40 mL/kg total blood products over 6 hours or were transfused under massive transfusion protocol were included. Interventions Children were compared according bleeding etiology: trauma, operative, or medical. Measurements and main results Patient characteristics, therapies administered, and clinical outcomes were analyzed. Among 449 enrolled children, 55.0% were male, and the median age was 7.3 years. Bleeding etiology was 46.1% trauma, 34.1% operative, and 19.8% medical. Prior to the life-threatening bleeding event, most had age-adjusted hypotension (61.2%), and 25% were hypothermic. Children with medical bleeding had higher median Pediatric Risk of Mortality scores (18) compared with children with trauma (11) and operative bleeding (12). Median Glasgow Coma Scale scores were lower for children with trauma (3) compared with operative (14) or medical bleeding (10.5). Median time from bleeding onset to first transfusion was 8 minutes for RBCs, 34 minutes for plasma, and 42 minutes for platelets. Postevent acute respiratory distress syndrome (20.3%) and acute kidney injury (18.5%) were common. Twenty-eight-day mortality was 37.5% and higher among children with medical bleeding (65.2%) compared with trauma (36.1%) and operative (23.8%). There were 82 hemorrhage deaths; 65.8% occurred by 6 hours and 86.5% by 24 hours. Conclusions Patient characteristics and outcomes among children with life-threatening bleeding varied by cause of bleeding. Mortality was high, and death from hemorrhage in this population occurred rapidly.

Background. In early 2020, the novel coronavirus pandemic forced communities around the globe to shut down and isolate. Routine graduate medical education activities have also been suspended as resident and fellow physicians-in-training have been re-deployed to support critical patient care services. Innovation. We developed a two-part hybrid telesimulation model to teach COVID-19 ventilator management strategies while physically separating a group of learners and an instructor from one another. Learners consisted of non-ICU health care providers with limited experience in ventilator management being redeployed to manage ICU level COVID-19 infected patients. In the first week, the video tutorial has been viewed over 500 times and we have facilitated 14 telesimulation sessions, including 48 participants comprised of hospitalists, emergency medicine physicians and physician assistants, pediatric residents, nurses, and a nurse educator. Conclusion. We believe that the combination of a video tutorial followed by an interactive telesimulation was successful in providing timely education during a coronavirus pandemic. Furthermore, it reinforced the value and flexibility in which simulation education could continue conveniently for learners despite significant restrictions in place during the coronavirus pandemic. Research is needed to assess the efficacy of this hybrid intervention in preparing healthcare workers and to determine if the knowledge is successfully transferred to the clinical setting.

OBJECTIVES: We describe the process by which a PICU and a PICU care team were incorporated into a hospital-wide ICU care model during the coronavirus disease 2019 pandemic. DESIGN: A descriptive, retrospective report from a single-center PICU. SETTING: Twenty-three bed, quaternary PICU, within an 862-bed hospital. PATIENTS: Critically ill adults, with coronavirus disease 2019-related disease. INTERVENTIONS: ICU care provided by pediatric intensivists with training and support from medical intensivists. MEASUREMENTS AND MAIN RESULTS: Within the context of the institution's comprehensive effort to centralize and systematize care for adults with severe coronavirus disease 2019 disease, the PICU was transitioned to an adult coronavirus disease 2019 critical care unit. Nurses and physicians underwent just-in-time training over 3 days and 2 weeks, respectively. Medical ICU physicians and nurses provided oversight for care and designated hospital-based teams were available for procedures and common adult emergencies. Over a 7-week period, the PICU cared for 60 adults with coronavirus disease 2019-related critical illness. Fifty-three required intubation and mechanical ventilation for a median of 18 days. Eighteen required renal replacement therapy and 17 died. CONCLUSIONS: During the current and potentially in future pandemics, where critical care resources are limited, pediatric intensivists and staff can be readily utilized to meaningfully contribute to the care of critically ill adults.

We consider the possibility that the preons defined by the SLq(2) extension of the Standard Model may be identified with Schwinger dyons. The SLq(2) extension is here presented as a model that may exist in either a currently observable electric phase or in a magnetic phase that is predicted but currently unobservable., Comment: arXiv admin note: text overlap with arXiv:1511.07919 and substantial text overlap with arXiv:1809.03324

We examine a generic field theory in which the field particle has two couplings. It is of particular interest when these are the electroweak, e, and the hypothetical magnetoweak, g. The new field operators are obtained by replacing the field operators $\Psi (x)$ of the standard model or of similar models by $\tilde{\Psi} (x) D^j_q (m,m')$ where $ D^j_q (m,m')$ is an element of the $2j+1$ dimensional representation of the SLq(2) algebra, which is also the knot algebra. The field is assumed to exist in two phases distinguished by two values of $q$: $q_e = \frac{e}{g}$ and $q_g = \frac{g}{e}$ which label the electroweak and magnetoweak phases respectively. We assume that the observed leptons and quarks are composed of e-preons and are in agreement with the observed charge spectrum of leptons and quarks. It is now proposed that there is also a g-phase where g-leptons and g-quarks are composed of g-preons. It is assumed that the g-charge is very large compared to the e-charge and the mass of the g charged particle is even larger since the mass of all of these particles is partially determined by the eigenvalues of $\bar{D}^j_q (m,m') D_q^j (m,m')$, a polynomial in $q$, that multiplies the Higgs mass term and where \begin{equation*} \frac{q_g}{q_e} = \left ( \frac{\hbar c}{e^2} \right)^2 \approx (137)^2. \end{equation*} These values of $q$ indicate that particles in the g-phase are much more massive, they should be harder to produce or to observe., Comment: arXiv admin note: substantial text overlap with arXiv:1511.07919

INTRODUCTION We have previously demonstrated that induction of profound hypothermia improves long-term survival in animal models of complex injuries/lethal hemorrhage. However, the precise mechanisms have not been well defined. The aim of this high-throughput study was to investigate the impact of profound hypothermia on gene expression profiles. METHODS Wistar-Kyoto rats underwent 40% blood volume arterial hemorrhage over 10 minutes and were randomized into two groups based on core body temperatures (n = 7 per group): hypothermia (H, 15 degrees C) and normothermia (N, 37 degrees C). Hypothermia was induced by infusing cold isotonic solution using a cardiopulmonary bypass (CPB) setup. After reaching target body temperature, low-flow state (CPB flow rate of 20 mL x kg x min) was maintained for 60 minutes. Hypothermic rats were rewarmed to baseline temperature, and all rats were resuscitated on CPB and monitored for 3 hours. The N group underwent identical CPB management. Sham rats (no hemorrhage and no instrumentation) were used as controls. Blood samples were collected serially, and hepatic tissues were harvested after 3 hours. Affymatrix Rat Gene 1.0 ST Array (27,342 genes, >700,000 probes) was used to determine gene expression profiles (n = 3 per group), which were further analyzed using GeneSpring (Agilent Technologies, Santa Clara, CA) and GenePattern (Broad Institute, Cambridge, MA) programs. Data were further queried using network analysis tools including Gene Ontology, and Ingenuity Pathway Analysis (Ingenuity Systems). Key findings were verified using real-time polymerase chain reaction and Western blots. RESULTS Induction of hypothermia significantly (p < 0.05) decreased the magnitude of lactic acidosis and increased the survival rates (100% vs. 0% in normothermia group). Five hundred seventy-one of 23,000 genes had altered expression in response to the induction of hypothermia: 382 were up-regulated and 187 were down-regulated. Twelve key pathways were specifically modulated by hypothermia. Interleukin-6, interleukin-10, p38 mitogen-activated protein kinase (MAPK), nuclear factor kappa-light-chain-enhancer of activated B cells, glucocorticoids, and other signaling pathways involved with acute phase reactants were up-regulated. Multiple metabolic pathways were down- regulated. The largest change was in the peroxisome proliferator-activated receptor gamma gene that codes for a transcriptional coactivator, which in turn controls mitochondrial biogenesis, glycerolipid, and other metabolic pathways in the liver. Apoptotic cell death cascades were activated in response to blood loss (H and N groups), but multiple specific anti-apoptotic genes (baculoviral Inhibitor of apoptosis protein repeat-containing 3, BCL3L1, NFKB2) displayed an increased expression specifically in the hypothermia treated animals, suggesting an overall pro-survival phenotype. CONCLUSIONS Profound hypothermia increases survival in a rodent model of hemorrhagic shock. In addition to decreasing tissue oxygen consumption, induction of hypothermia directly alters the expression profiles of key genes, with an overall up-regulation of pro-survival pathways and a down- regulation of metabolic pathways.

We study the replacement of SU(3) by SU q(3) in standard gauge theories. At the level of a global theory there is a physically sensible SU q(3) formalism with measurable differences from the SU (3) theory.

A gauged SU q (2) theory is characterized by two dual algebras, the first lying close to the Lie algebra of SU(2) while the second introduces new degrees of freedom that may be associated with nonlocality or solitonic structure. The first and second algebras, here called the external and internal algebras respectively, define two sets of fields, also called external and internal. The gauged external fields agree with the Weinberg–Salam model at the level of the doublet representation but differ at the level of the adjoint representation. For example, the g-factor of the charged W-boson differs in the two models. The gauged internal fields remain speculative but are analogous to color fields.

When the symmetry of a physical theory describing a finite system is deformed by replacing its Lie group by the corresponding quantum group, the operators and state function will lie in a new algebra describing new degrees of freedom. If the symmetry of a field theory is deformed in this way, the enlarged state space will again describe additional degrees of freedom, and the energy levels will acquire fine structure. The massive particles will have a stringlike spectrum lifting the degeneracy of the point-particle theory, and the resulting theory will have a non-local description. Theories of this kind naturally contain two sectors with one sector lying close to the standard theory while the second sector describes particles that should be more difficult to observe., Comment: 7 pages, TeX file

The connection between spin and statistics implied by the continuous Lorentz group together with strong reflection (TCP) is shown to hold also for the q-Lorentz group.

We use the Kerr–Schild formalism topresent a simple view of a rotating dyon which isneither multidimensional nor supersymmetric, and may beregarded as a correspondence limit of a string dyon. Inthis metric, which permits Minkowskian solutions, wefind that both in the Einstein and Landau prescriptionsthe pseudo-energy-momentum tensor vanishes, withoutassuming that the null vector is also geodesic, as was done in earlier work. This allows anessentially Lorentz covariant treatment of theequations. The calculation of the total mass and angularmomentum are presented for completeness and we find that the contribution of the angular momentum to themass appears in the condition for the appearance of ahorizon and leads to the known modifiedBogomolny–Prasad–Sommerfield (bps)relation.

Examples are given of q-deformed systems that may be interpreted by the standard rules of quantum theory in terms of new degrees of freedom and supplementary quantum numbers.

A general relativistic and nontopological soliton is constructed by coupling a nonlinear scalar field to the standard gravitational field. Our results replicate the basic features of the special relativistic case: namely, a singularity-free lump with a discrete spectrum of eigensolutions. The central singularities and horizon that appear in the black hole solitons of string theory are not present.

We have obtained in configuration space the state functions of the q-isotropic oscillator by laddering the state functions of the q-linear oscillator. Starting from the q-Hermite functions of the linear oscillator one obtains the q-associated Laguerre functions of the isotropic oscillator. The energy spectrum is obtained from the curvature of the wave function at a point where the potential energy vanishes.

The standard transform with a twisted q -kernel is proposed for connecting q -amplitudes in three-dimensional configuration space with those in three-dimensional momentum space.

There exist operator solutions of the q‐Coulomb problem in both configuration and momentum space. Since the arguments of the corresponding amplitudes are noncommuting, however, there are problems of physical interpretation. Here we answer the question of physical interpretation by associating with the operator amplitude in momentum space a numerically valued amplitude lying in a Hilbert space defined by the SUq(2) algebra. This new amplitude, now depending on commuting arguments, may be interpreted by the usual rules of quantum mechanics and may also be Fourier transformed to yield the amplitude in configuration space.

Our SLq(2) extension of the standard model is constructed by replacing the elementary field operators, $\Psi (x)$, of the standard model by $\hat{\Psi}^{j}_{mm'}(x) D^{j}_{mm'}$ where $D^{j}_{mm'}$ is an element of the $2j + 1$ dimensional representation of the SLq(2) algebra, which is also the knot algebra. The allowed quantum states $(j,m,m')$ are restricted by the topological conditions \begin{equation*} (j,m,m') = \frac{1}{2}(N,w,r+o) \end{equation*} postulated between the states of the quantum knot $(j,m,m')$ and the corresponding classical knot $(N,w,r+o)$ where the $(N,w,r)$ are (the number of crossings, the writhe, the rotation) of the 2d projection of the corresponding oriented classical knot. Here $o$ is an odd number that is required by the difference in parity between $w$ and $r$. There is also the empirical restriction on the allowed states \begin{equation*} (j,m,m')=3(t,-t_3,-t_0)_L \end{equation*} that holds at the $j=\frac{3}{2}$ level, connecting quantum trefoils $(\frac{3}{2},m,m')$ with leptons and quarks $(\frac{1}{2}, -t_3, -t_0)_L$. The so constructed knotted leptons and quarks turn out to be composed of three $j=\frac{1}{2}$ particles which unexpectedly agree with the preon models of Harrari and Shupe. The $j=0$ particles, being electroweak neutral, are dark and plausibly greatly outnumber the quarks and leptons. The SLq(2) or $(j,m,m')$ measure of charge has a direct physical interpretation since $2j$ is the total number of preonic charges while $2m$ and $2m'$ are the numbers of writhe and rotation sources of preonic charge. The total SLq(2) charge of a particle, measured by writhe and rotation and composed of preons, sums the signs of the counterclockwise turns $(+1)$ and clockwise turns $(-1)$ that any energy-momentum current makes in going once around the knot... Keywords: Quantum group; electroweak; knot models; preon models; dark matter., Comment: 21 pages, 3 figures. arXiv admin note: text overlap with arXiv:1401.1833

We obtain the complete set of states of theq-oscillator in both configuration space and momentum space as well as the transformation between these spaces. The states as well as the matrix elements lie in the SU q (2) algebra. To obtain transition probabilities, one must take the ‘Woronowicz square.’

Although there is no empirical motivation for replacing the commutators of dynamically conjugate operators in quantum mechanics byq-commutators, it appears possible to construct a consistent mathematical formulism based on this idea. To examine such a possibility further, we have studied the relation of this proposal to the Schwinger action principle, since the entire quantum mechanical formulism may be inferred from this principle. In particular, we have discussed the quantum transformation theory within this framework.

A deformation of quantum mechanics obtained by replacing commutators by q‐commutators (where q is close enough to unity to be compatible with experiment) is studied. This idea is explored by studying the q‐harmonic oscillator in both configuration space and momentum space. The complete set of states in both representations as well as the transformation between x and p space is obtained. The states as well as the matrix elements lie in the SUq(2) algebra. To obtain expectation values and transition probabilities one must average over the SUq(2) algebra.

One may attempt to implementq-symmetry in field theory by replacing commutators byq-commutators. The quantized field is then described byq-oscillators. This program encounters a basic difficulty, however, when one demands either causality or consistency between the twin requirements of causality and positive energy. Independent of the preceding remark, one notes that the Einstein-Bose and Fermi-Dirac thermal distributions appear as limiting cases of the quantizedq-field whenq = ± 1.

We calculate the Clebsch-Gordan coefficients of SUq(2) by a Woronowicz integration over the group manifold and obtain a representation differing from that reached by working with theq-group algebra. These apparently different results must agree, however, and their equivalence implies aq-identity. On lettingq = 1, we shall obtain two results of different structures for the Clebsch-Gordan coefficients of SU(2) and their equivalence similarly implies an identity among the usual binomial coefficients. With the same approach, one may extend the Woronowicz integral of the product of two irreducible representations to products of many irreducible representations.

The orthogonality relations for SUq(2) are here formulated with the aid of the Woronowicz integral. The first part of this paper is devoted to a summary of the relevant parts of the Woronowicz theory and the second part to its implementation in terms of completely explicit representations of the irreducible unitary representations. The purpose of this presentation is to provide background for a separate study of the q deformation of the Coulomb problem.

The hydrogenic Schrodinger equation may be transformed into an integral equation on the group space of SO(3). The solutions of this integral equation are the Wigner functions Djmn, the matrix elements of the irreducible representations of SO(3). In this article we examine a q‐deformation of the Coulomb problem for which the new wave functions are the matrix elements of the irreducible representations of the quantum group SUq(2). The new integral equation is formulated in terms of the Woronowicz integral. The eigenvalues are given by a modified Balmer formula which lifts the Coulomb degeneracy and replaces n by [n].

We present some partial results on theq-deformation of the GL(2) Yang-Mills theory. In particular, the irreducible representations needed to describe the complete set of physical states are obtained by a simple procedure.

The Grassmannian analogues of the Legendre polonomials are obtained from the corresponding Grassmannian Hermite multinomials. The generating function, recurrence relations, and differential equation are given. In contrast to the Hermitian case there is no Berezin weight function that orthogonalizes these functions. Generalizations to the Tchebyscheff and Gegenbauer cases are also possible.

An affine field theory may be constructed by gauging an affine algebra. The momentum integrals of the affine N = 4 Yang–Mills theory are ultraviolet finite but diverge because the sum over states is infinite. If the affine symmetry is broken by postulating a nonvanishing vacuum expectation value for that component of the scalar field lying in the L0 direction, then the theory acquires a linear mass spectrum. This broken theory is ultraviolet finite too, but the mass spectrum is unbounded. If it is also postulated that the mass spectrum has an upper bound (say, the Planck mass), then the resulting theory appears to be altogether finite. The influence of the exotic states has been estimated and, according to the proposed scenario, is negligible below energies at which gravitational interactions become important. The final effective theory has the symmetry of a compact Lie algebra augmented by the operator L0.

By generalizing from systems characterized by finite Lie algebras the propagator of an extended particle that appears in a gauge theory based on an affine algebra is discussed.

We examine the propagators associated with particles characterized by an internal symmetry. Of particular interest is the case of spontaneously broken Kac-Moody algebra.

It is shown that the four trefoil solitons that are described by the irreducible representations D^{3/2}_{mm'} of the quantum algebra SL_q(2) (and that may be identified with the four families of elementary fermions (e,\mu,\tau;\nu_e\nu_\mu\nu_\tau;d,s,b;u,c,t) may be built out of three preons, chosen from two charged preons with charges (1/3,-1/3) and two neutral preons. These preons are Lorentz spinors and are described by the D^{1/2}_{mm'} representation of SL_q(2). There are also four bosonic preons described by the D^1_{mm'} and D^0_{00} representations of SL_q(2). The knotted standard theory may be replicated at the preon level and the conjectured particles are in principle indirectly observable., Comment: LaTex document; 12 pages; 4 tables

We explore a knot model of the elementary particles that is compatible with electroweak physics. The knots are quantized and their kinematic states are labelled by $D^j_{mm'}$, irreducible representations of $SU_q(2)$, where j = N/2, m = w/2, m' = (r+1)/2 and (N,w,r) designate respectively the number of crossings, the writhe, and the rotation of the knot. The knot quantum numbers (N,w,r) are related to the standard isotopic spin quantum numbers $(t,t_3,t_0)$ by $(t=N/6,t_3=-w/6,t_0=-(r+1)/6)$, where $t_0$ is the hypercharge. In this model the elementary fermions are low lying states of the quantum trefoil (N=3) and the gauge bosons are ditrefoils (N=6). The fermionic knots interact by the emission and absorption of bosonic knots. In this framework we have explored a slightly modified standard electroweak Lagrangian with a slightly modified gauge group which agrees closely but not entirely with standard electroweak theory., Comment: 29 pages; LaTex file

The idea that the elementary particles might have the symmetry of knots has had a long history. In any modern formulation of this idea, however, the knot must be quantized. The present review is a summary of a small set of papers that began as an attempt to correlate the properties of quantized knots with empirical properties of the elementary particles. As the ideas behind these papers have developed over a number of years, the model has evolved, and this review is intended to present the model in its current form. The original picture of an elementary fermion as a solitonic knot of field, described by the trefoil representation of SUq(2), has expanded into its present form in which a knotted field is complementary to a composite structure composed of three preons that in turn are described by the fundamental representation of SLq(2). Higher representations of SLq(2) are interpreted as describing composite particles composed of three or more preons bound by a knotted field. This preon model unexpectedly agrees in important detail with the Harari–Shupe model. There is an associated Lagrangian dynamics capable in principle of describing the interactions and masses of the particles generated by the model.

The q-electroweak theory suggests a description of elementary particles as solitons labelled by the irreducible representations of SU_q(2). Since knots may also be labelled by the irreducible representations of SU_q(2), we study a model of elementary particles based on a one-to-one correspondence between the four families of Fermions (leptons, neutrinos, (-1/3) quarks, (2/3) quarks) and the four simplest knots (trefoils). In this model the three particles of each family are identified with the ground and first two excited states of their common trefoil. Guided by the standard electroweak theory we calculate conditions restricting the masses of the fermions and the interactions between them. In its present form the model predicts a fourth generation of fermions as well as a neutrino spectrum. The same model with q almost equal to 1 is compatible with the Kobayashi-Maskawa matrix. Depending on the test of these predictions, the model may be refined., Comment: 40 pages, 2 figures, latex format

We attempt to go beyond the standard electroweak theory by replacing SU(2) with its q-deformation: SU_q(2). This step introduces new degrees of freedom that we interpret as indicative of non-locality and as a possible basis for a solitonic model of the elementary particles. The solitons are conjectured to be knotted flux tubes labelled by the irreducible representations of SU_q(2), an alglebra which is not only closely related to the standard theory but also plays an underlying role in the description of knots. Each of the four families of elementary fermions is conjectured to be represented by one of the four possible trefoils. The three individual fermions belonging to any family are then assumed to occupy the three lowest states in the excitation spectrum of the local trefoil for that family. One finds a not unreasonable variation of q among the lepton and quark families. The model in its present form predicts a fourth generation of fermions as well as a neutrino mass spectrum. The model may be refined depending on whether or not the fourth generation is found., 10 pages, Latex file; changed content

There are suggestive experimental indications that the leptons, neutrinos, and quarks are composite and that their structure is described by the quantum group SLq(2). Since the hypothetical preons must be very heavy relative to the masses of the leptons, neutrinos, and quarks, there must be a very strong binding field to permit these composite particles to form. Unfortunately there are no experiments direct enough to establish the order of magnitude needed to make the SLq(2) Lagrangian dynamics quantitative. It is possible, however, to parametrize the preon masses and interactions that would be necessary to stabilize the three particle composite representing the leptons, neutrinos, and quarks. In this note we examine possible parametrizations of the masses and the interactions of these hypothetical structures. We also note an alternative view of SLq(2) preons., arXiv admin note: text overlap with arXiv:1301.6440

We have examined the deformation of a generic non-Abelian gauge theory obtained by replacing its Lie group by the corresponding quantum group. This deformed gauge theory has more degrees of freedom than the theory from which it is derived. By going over from point particles in the standard theory to solitonic particles in the deformed theory, it is proposed to interpret the new degrees of fredom as descriptive of a non-locality of the deformed theory. It also turns out that the original Lie algebra gets replaced by two dual algebras, one of which lies close to and approaches the original Lie algebra in a correspondence limit, while the second algebra is new and disappears in this same correspondence limit. The exotic field particles associated with the second algebra can be interpreted as quark-like constituents of the solitons, which are themselves described as point particles in the first algebra. These ideas are explored for q-deformed SU(2) and $GL_q(3)$., Comment: 26 pages, TeX file, Revised Version

The straightforward description of q-deformed systems leads to transition amplitudes that are not numerically valued. To give physical meaning to these expressions without introducing ad hoc remedies, one may exploit an “internal” Fock space already defined by the q-algebra. This internal space may be interpreted in terms of internal degrees of freedom of the deformed system or alternatively in terms of non-locality. It is shown that the q-deformation may give stringy characteristics to a Yang-Mills theory.

As one would anticipate from the realization of the q-commutators by difference operators, the states of maximum localization are smeared delta functions depending on q., Comment: 10 pages, tex file

We describe a q-deformation of the Lorentz group in terms of a q-deformation of the van der Waerden spinor algebra., Comment: Tex file, 17 pages

We examine some issues that arise in the q-deformation of a gauge theory. If the deformation is carried out by replacing the equal time commutators of free fields by the corresponding q-commutators, the resulting propagators are not very much different from those of the undeformed theory as long as one is dealing with weak fields; but the theory still violates causality. If one postulates a q-deformed S matrix, the corresponding q-causal commutator has 2 poles of different strength and the result again amounts to a deformation of the Lorentz group., Comment: Tex file, 18 pages

It is possible to construct non-Abelian field theories by gauging Kac-Moody algebras. Here we discuss the spontaneous symmetry breaking of such theories via the Higgs mechanism. If the Higgs particle lies in the Cartan subalgebra of the Kac-Moody algebra, the previously massless vectors acquire a mass spectrum that is linear in the Kac-Moody index and has additional fine structure depending on the associated Lie algebra.

The gravitational and electromagnetic fields of a charged, rotating source are obtained by an elementary algebraic method.

We describe an algorithm to solve the classical equations of supergravity for the coupled fields of helicity 2 and 3/2. The algorithm depends on an expansion in the associated Grassman algebra and leads to a sequence of coupled equations that may be solved in a step by step manner. The procedure begins with solutions of the usual empty space Einstein equations but the subsequent equations are all linear differential equations. To complete the method, it is necessary to generalize the supplementary conditions on the vector spinor field from flat to curved space. The algorithm also permits a classification of the complete solutions in terms of the associated gravitational fields. It is shown that vanishing curvature implies Minkowski space and does not permit other conceivable possibilities such as a Clifford space. Generalizations of the vanishing curvature space are suggested.

In an earlier source theory investigation it was shown that the vacuum polarization of a massive gauge field is finite, provided that the conservation of current is imposed everywhere, including the interior of the sources. It is shown in the present paper that radiative corrections to a vertex function (two-particle production by an external source) are also finite if the same requirement about current conservation is imposed. In other words one-loop corrections turn out to be finite in both calculations. The cancellations leading to convergence may be understood in terms of Ward identities. The three form factors that appear are not only shown to be finite but are also explicity found.

It is shown that there is no obstacle to the affine extension of supersymmetric Yang-Mills theories. This result holds equally for loop and Kac-Moody algebras. It also holds for 4, 6, and 10 dimensions. By dimensional reduction of the 10-dimensional theory one obtains a supersymmetric action describing interacting Kac-Moody fields in four dimensions.

We construct a non-Abelian field theory by gauging a Kac-Moody algebra. One obtains an infinite tower of interacting vector fields and associated ghosts obeying slightly modified Feynman rules.