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We delve into the first principles of quantum field theory to prove that the so-called spin-1/2 ''bosons'' and the fermions with mass dimension 1, including ELKO, cannot represent physical particle states with spin $1/2$. Specifically, we first demonstrate that both aforementioned fields are not invariant under rotational symmetry, which implies that the particles created for these fields are not eigenstates of the spin operator in the $(\frac{1}{2},0)\oplus(0,\frac{1}{2})$ representation of the Lorentz group, nor is it possible to construct a Hamiltonian density scalar under the rotational group from them. Furthermore, following Weinberg's approach to local causal fields, we prove that regardless of any discrete symmetry or adjoint structure, the relativistic fields in the $(\frac{1}{2}, 0) \oplus (0,\frac{1}{2})$ representation satisfy the Fermi-Dirac statistics in complete agreement with the well-established spin-statistics theorem and experimental results., Comment: 9 pages

Axion electrodynamics is based upon the Lagrangian of the electromagnetic (EM) field plus its interaction with the axions, and is accordingly a physically open system. It means that the four-divergence of the EM energy-momentum tensor is different from zero, implying in turn that the total EM energy and momentum (when integrated over all space) do not constitute a four-vector. The EM force is in principle accessible to experimental detection, just analogous to what is the case in ordinary electrodynamics. In the first half of this paper the energy-momentum aspects of axion electrodynamics are worked out in general, when the surroundings are allowed to be a medium with constant permittivity and permeability. In the second half, two examples are discussed. The first is a static situation, where a block of uniform material containing axions is exposed to external strong electric and magnetic fields. Assuming the axion amplitude $a(x)$ (i.e. its density) to increase linearly in one direction, we calculate the axion-generated forces. As a second example, we consider axions varying not with position but instead harmonically with time; this is the constellation usually assumed in astrophysics. Assuming a Gaussian profile for the EM wave emitted from the Earth towards an axion cloud in outer space, we make a calculation of the 'axion echo', the return signal., Comment: 19 pages latex, slightly extended version. To appear in Int. J. Mod. Phys. A

A new electromagnetism is still expected to be developed. Thus, under such a principlewhere nature works as a group, an electromagnetism beyond Maxwell is studied. It considersthat light metric antecedes electric charge for founding the EM phenomena. Based on wholenessprinciple, Lorentz group and gauge invariance this electromagnetism sticked on light is proposed.Then, by electromagnetism it will be understood the physics derived from Lorentz group potentialfields family (for simplicity other fields are not included). New electromagnetic fields,sectors, layers and regimes are developed. It yields a branch with transversal and longitudinalEM fields, granular and collective sectors, I-fields layers and four regimes (photonic, massive,neutral, charged) connected through a global photon. Their relationships are determined by astate equation identified as Global Maxwell equation. It contains new Gauss and Ampere laws,exclusive Faraday law for polarization and magnetization vectors, divergenceless magnetizationvector having fields as sources, self-interacting photons mediated by a dimensionless couplingconstant and other features. It is complemented by a Global Lorentz equation which besidesthe usual Lorentz force add forces depending on mass and on potential fields.

Color confinement is one of the central issues in QCD so that there are various interpretations of this feature. In this paper we have adopted the interpretation that colored particles are not subject to observation just because colored states are unphysical in the sense of Eq. (2.16). It is shown that there are two phases in QCD distinguished by different choices of the gauge parameter. In one phase, called the "confinement phase", color confinement is realized and gluons turn out to be massive. In the other phase, called the "deconfinement phase", color confinement is not realized, but the gluons remain massless.

We study the single production of scalar neutrinos or charginos via $\gamma\gamma$ collision in an R-parity ($R_{p}$) violating supersymmetric model. It may be possible to detect a sneutrino or a chargino at a Linear Collider (LC) in $\gamma \gamma$ operation mode, as a test of supersymmetry and $R_p$-violation. Because of the clean background in LC, stringent constraints on $R_p$ violating parameters can be obtained even if the process cannot be observed at the future Linear Collider.

Recently, developments in the understanding of low-energy N=1 supersymmetric gauge theory have revealed two important phenomena: the appearance of new four-dimensional superconformal field theories and a non-Abelian generalization of electric-magnetic duality at the IR fixed point. This report is a pedagogical introduction to these phenomena. After presenting some necessary background material, a detailed introduction to the low-energy non-perturbative dynamics of N=1 supersymmetric $SU(N_c)$ QCD is given. The emergence of new four-dimensional superconformal field theories and non-Abelian duality is explained. New non-perturbative phenomena in supersymmetric $SO(N_c)$ and $Sp(N_c=2n_c)$ gauge theories, such as the two inequivalent branches, oblique confinement and electric-magnetic-dyonic triality, are presented. Finally, some new features of these four-dimensional superconformal field theories are exhibited: the universal operator product expansion, evidence for a possible $c$-theorem in four dimensions and the critical behaviour of anomalous currents. The concluding remarks contain a brief history of electric-magnetic duality and a discussion on the possible applications of duality to ordinary QCD., Comment: 239 pages, LaTex 2-3 times, 4 eps files

The generalized Cremmer-Gervais R-matrix, which is a twist of the standard slq (3) R-matrix, depends on two additional parameters. We discuss the properties of this R-matrix and construct two associated dynamic systems: the q-oscillator that is covariant with respect to the corresponding quantum group and an integrable spin chain with a non-Hermitian Hamiltonian.

The evolution of QCD coupling constant at finite temperature is considered by making use of the finite temperature renormalization group equation up to the one-loop order in the background field method with the Feynman gauge and the imaginary time formalism. The results are compared with the ones obtained in the literature. We point out, in particular, the origin of the discrepancies between different calculations, such as the choice of gauge, the breakdown of Lorentz invariance, imaginary versus real time formalism and the applicability of the Ward identities at finite temperature.

It is shown that a particular $q$-deformation of the Virasoro algebra can be interpreted in terms of the $q$-local field $\Phi (x)$ and the Schwinger-like point-splitted Virasoro currents, quadratic in $\Phi (x)$. The $q$-deformed Virasoro algebra possesses an additional index $\alpha$, which is directly related to point-splitting of the currents. The generators in the $q$-deformed case are found to exactly reproduce the results obtained by probing the fields $X(z)$ (string coordinate) and $\Phi (z)$ (string momentum) with the non-splitted Virasoro generators and lead to a particular representation of the $SU_q (1,1)$ algebra characterized by the standard conformal dimension $J$ of the field. Some remarks concerning the $q$-vertex operator for the interacting $q$-string theory are made.

The lepton number violating process $\mu\rightarrow e\gamma$ is used to study the lepton number violating couplings in MSSM extended by terms violating $R$-parity explicitly. Bounds are obtained for the products of $\lambda $- or $\lambda '$-type couplings. It is found that many of these limits are more stringent than the ones obtained previously.

We classify the unitary representations of the extended Poincar\'e supergroups in three dimensions. Irreducible unitary representations of any spin can appear, which correspond to supersymmetric anyons. Our results also show that all irreducible unitary representations necessarily have physical momenta. This is in sharp contrast to the ordinary Poincar\'e group in three dimensions, that admits in addition irreducible unitary representations with non-physical momenta, which are discarded on physical grounds., Comment: 7 pages; commentaries added in Sect. IV A and in Conclusion; added references

The classification of the second-class constraints in the framework of the total Hamiltonian formalism is presented. The structure of the second-class constraint chains is studied in detail and a graphical representation is given.

We discuss some aspects of the CP violation measurements of neutral B mesons using time-dependent decay rates. We consider pp processes in which B0 and B 0 may not be produced in equal amounts. We study in details the case of Bd0, B d 0 mesons decaying into a self-conjugate state. The method proposed could have implications in planning experiments at LHC and SSC.

We construct a realization of the q-deformed anti-de Sitter algebra in terms of two q-oscillators. We use the standard Drinfel'd-Jimbo prescription for the q-deformation of the Chevalley basis which we express in terms of q-oscillators. We also discuss the anti-de Sitter radius R → ∞ limit and the structure of the first so (3, 2)q Casimir operator.

Starting from the axiomatic field-theory principles (analyticity, unitarity and polynomial boundedness) we obtain high-energy bounds on the amplitude of elastic scattering in a space-time of general dimension D. This is of interest due to recently developed theories in higher dimensions. A comparison of our bounds (which are rigorously valid only for a theory with a mass gap) with the high-energy behaviour of string amplitude, summed up to all loops by Amati, Ciafaloni and Veneziano, shows that σinel saturates our bound, while consistency with the behaviour of σtot requires D ⩾ 6 and a fast shrinking of the analyticity ellipse (which might indicate nonlocality of the string theory). This behaviour of σtot is due to massless graviton exchange and violates our bounds if no shrinking of the analyticity ellipse is assumed. Our fixed-angle bound, however, is obeyed by the high-energy fixed-angle behaviour of elastic string scattering amplitudes in all orders obtained by Mende and Ooguri. We also show that analyticity of the amplitude in s leads to the well-known extension of the analyticity domain. Alternatives to polynomial boundedness (relevant to string theories) are also discussed.

Following the methods of statistical quantum electrodynamics, a heuristic model for relativistic fractional quantum Hall effect is proposed based on three fundamental assumptions: constancy of the chemical potential, fractional Landau quantum numbers due to anyonic effects, and fractional Fermi-Dirac statistics for anyons. The model explains the well-established experimental fact that the plateau extrema of the quantized conductivity are precisely proportional to the inverse filling factors q p .

We propose to take advantage of using the Wiener path integrals as the formal solution for the joint probability densities of coupled Langevin equations describing particles suspended in a fluid under the effect of viscous and random forces. Our obtained formal solution, giving the expression for the Lyapunov exponent, i) will provide the description of all the features and the behaviour of such a system, e.g. the aggregation phenomenon recently studied in the literature using appropriate approximations, ii) can be used to determine the occurrence and the nature of the aggregation - non-aggregation phase transition which we have shown for the one-dimensional case and iii) allows the use of a variety of approximative methods appropriate for the physical conditions of the problem such as instanton solutions in the WKB approximation in the aggregation phase for the one-dimensional case as presented in this paper. The use of instanton approximation gives the same result for the Lyapunov exponent in the aggregation phase, previously obtained by other authors using a different approximative method. The case of non-aggregation is also considered in a certain approximation using the general path integral expression for the one-dimensional case., Comment: 18 pages; added section III C containing WKB method (instanton approximation) for the evaluation of the path integral in the aggregation, as well as non-aggregation, phases

It is argued that the free-electron wave functions in crossed magnetic and electric fields exactly diagonalize the full propagator for the Coulomb interacting electron gas. The result follows under the assumption that the translational invariance is unbroken in the ground state. We derive this property for the 2D electron gas, usually discussed in QHE context. This property is also valid for the general 3D electron systems retaining translational invariance in the plane orthogonal to the magnetic field. A simple diagonalized formula for the propagator is also presented.

We describe the q -deformations of the realisations of the conformal algebra depending on the conformal dimension parameter Δ . The particular role of the conformal dimensions Δ=0, 1 2 , 1 is pointed out. The q -deformed central extension terms, describing q -deformation of the Virasoro algebra, are derived. In the limit q → 1 one obtains the usual central term. The transformation properties of the q -deformed energy-momentum tensor ( Δ =2) consistent with the q -deformed central extension term are described.

We construct the q-superoscillator algebra of n bosonic and m fermionic q-oscillators covariant under the coactions of the quantum supergroup SUq(n\)-invariant form bilinear in q-superoscillator variables describes the q-deformation of the hamiltonian for the supersymmetric oscillator in quantum mechanics. It is shown that such a hamiltonian is also invariant under the action of the U q ( U (n\m)) superalgebra, generated by the bilinears constructed from the q-superoscillators. The simplest case n=m=1 is considered in detail. The formulae relating the supercovariant q-oscillators with the independent ones are given.

A new derivation of the Faddeev-Popov path integral is presented. The use of gauge invariant transformations and gauge fixing conditions in the phase space allows to introduce straightforwardly Lorentz invariant gauge conditions into the path integral, thus avoiding the necessity of going first through a Coulomb-like gauge as it is usually done. The case of systems with finite degrees of freedom and the abelian (QED) one are also presented for illustration.

In the framework of Quantum Field Theory (QFT) on noncommutative (NC) space-time with SO(1,l) x SO(2) symmetry and space-space noncommutativity (Ooi = 0), we prove that, based on the causality condition usually taken in connection with this symmetry, it is merely impossible to draw any conclusion on the analyticity of the 2 + 2scattering amplitude in cos 0, 0 being the scattering angle. A physical choice of the causality condition rescues the situation and as a result an analog of Lehmann’s ellipse as domain of analyticity in cos 8 is obtained. However, the enlargement of this analyticity domain to Martin’s ellipse and the derivation of the Froissart bound for the total cross section in NC QFT is possible only in the special case when the incoming momentum is orthogonal to the NC plane. This is the first example of a nonlocal theory in which the cross sections are subject to a high-energy bound.

It is shown that a sufficient condition for color confinement is given by Z_3^{-1}=0, where Z_3 denotes the renormalization constant of the color gauge field., 7 pages, talk given at the International workshop "Strong Coupling Gauge Theories and Effective Field Theories", December 2002, Nagoya, Japan

The conservation of charge in a classical field theory is considered. It is shown that when the initial field configuration has finite energy, the charge can be non-conserved in some cases, among which are those where the quantum theory would exhibit spontaneous symmetry breakdown by the Goldstone mechanism.

We perform two-loop calculation of Chern-Simons in background field method using the hybrid regularization of higher-covariant derivative and dimensional regularization. It is explicitly shown that Chern-Simons field theory is finite at the two-loop level. This finiteness plays an important role in the relation of Chern-Simons theory with two-dimensional conformal field theory and the description of link invariant., RevTex, 13 pages. The proof of the existence of the large topological mass limit has been proved. Some typewritten mistakes have been corrected

The meaning of quantum group transformation properties is discussed in some detail by comparing the (co)actions of the quantum group with those of the corresponding Lie group, both of which have the same algebraic (matrix) form of the transformation. Various algebras are considered which are covariant with respect to the quantum (super) groups $SU_q(2),\; SU_q(1, 1),\; SU_q(1|1),\; SU_q(n), \\ SU_q(m|n),\; OSp_q(1|2)$ as well as deformed Minkowski space-time algebras.

Renormalization in quantum statistics in the presence of a charge associated to a spontaneously broken symmetry is discussed for the scalar field model. In contrast to the case of non-broken symmetry, the renormalization mass counterterm depends on the chemical potential. We argue that this is connected to the ill-defined character of the charge operator., 7 pages (plain TeX), HU-SEFT R 1993-8. (Offending bold greek removed)

Assuming that there exist operators which form an irreducible representation of the q-superoscillator algebra, it is proved that any two such representations are equivalent, related by a uniquely determined superunitary transformation. This provides with a q-supersymmetric generalization of the well-known uniqueness theorem of von Neumann for any finite number of degrees of freedom., 10 pages, Latex, HU-TFT-93-28

We propose a model for spontaneous $R$-parity breaking based on a simple extension of the minimal low energy supergravity model. We also consider the temperature effects in the scalar potential and show that a phase transition for the breaking of $R$ parity could have occurred in the early Universe later than the gauge symmetry breaking. This constraint is imposed on the extensions of the standard model which violate baryon and/or lepton number in order to explain the existing baryon asymmetry of the Universe. Otherwise, any previously established baryon asymmetry could be washed away.