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This paper provides a review of the literature on rigorous definitions and constructions in quantum field theory (QFT), spanning the period of seven decades. Compared with the ideas and constructions found in the modern physics literature, we conclude that none of the existing systems of QFT axioms can cover all the physical situations. Therefore, it is still an outstanding open problem to formulate a complete definition of QFT. We argue that the question is of relevance for both physicists and mathematicians. [ABSTRACT FROM AUTHOR]

In his paper, Einstein derived ΔL = Δmc² (light energy-mass equation). It has not been completely studied; it is only valid under special conditions of the parameters involved, e.g., number of light waves, magnitude of light energy, angles at which waves are emitted and relative velocity v. Einstein considered just two light waves of equal energy, emitted in opposite directions and the relative velocity v uniform. There are numerous possibilities for the parameters which were not considered in Einstein's derivation. ΔE = Δmc2 is obtained from ΔL = Δmc² by simply replacing L by E (all energy) without derivation. Fadner [Am. J. Phys. 56, 144 (1988)] correctly pointed out that Einstein neither mentioned E or ΔE = Δmc² in the derivation. Herein additional results are critically analyzed, taking all possible variables into account. Under some valid conditions of parameters, ΔL = ΔDmc² is not obtained, e.g., sometimes the result is Ma = Mb or no equation is derivable. If all values of valid parameters are taken into account, then the same derivation also gives L ∝ Δmc² or L = A Δmc², where A is a coefficient of proportionality. Thus, Einstein's derivation under valid parameters also predicts that energy emitted may be less than or more than ΔL = Δmc². [ABSTRACT FROM AUTHOR]

The scattering matrix (S-matrix), relating the initial and final states of a physical system undergoing a scattering process, is a fundamental object in quantum mechanics and quantum field theory. The study of factorized S-matrices, in which many-body scattering factorizes into a product of two-body terms to yield an integrable model, has long been considered the domain of mathematical physics. Many beautiful results have been obtained over several decades for integrable models of this kind, with far reaching implications in both mathematics and theoretical physics. The viewpoint that these were only toy models changed dramatically with brilliant experimental advances in realizing low-dimensional quantum many-body systems in the lab. These recent experiments involve both the traditional setting of condensed matter physics and the trapping and cooling of atoms in optical lattices to engineer and study quasi-one-dimensional systems. In some cases the quantum physics of one-dimensional systems is arguably more interesting than their three-dimensional counterparts, because the effect of interactions is more pronounced when atoms are confined to one dimension. This article provides a brief overview of these ongoing developments, which highlight the fundamental importance of integrability. [ABSTRACT FROM AUTHOR]

In this paper we discuss dilaton shifts (Euler counterterms) arising in decomposition of two-dimensional quantum field theories with higher-form symmetries. Relative shifts between universes are fixed by locality and take a universal form, reflecting underlying (noninvertible, quantum) symmetries. The first part of this paper constructs a general formula for such dilaton shifts, and discusses related computations. In the second part of this paper, we comment on the relation between decomposition and ensembles. [ABSTRACT FROM AUTHOR]

In a seminal work, Hawking showed that natural states for free quantum matter fields on classical spacetimes that solve the spherically symmetric vacuum Einstein equations are KMS states of non-vanishing temperature. Although Hawking's calculation does not include the backreaction of matter on geometry, it is more than plausible that the corresponding Hawking radiation leads to black hole evaporation which is, in principle, observable. Obviously, an improvement of Hawking's calculation including backreaction is a problem of quantum gravity. Since no commonly accepted quantum field theory of general relativity is available yet, it has been difficult to reliably derive the backreaction effect. An obvious approach is to use the black hole perturbation theory of a Schwarzschild black hole of fixed mass and to quantize those perturbations. However, it is not clear how to reconcile perturbation theory with gauge invariance beyond linear perturbations. In recent work, we proposed a new approach to this problem that applies when the physical situation has an approximate symmetry, such as homogeneity (cosmology), spherical symmetry (Schwarzschild), or axial symmetry (Kerr). The idea, which is surprisingly feasible, is to first construct the non-perturbative physical (reduced) Hamiltonian of the reduced phase space of fully gauge invariant observables and only then apply perturbation theory directly in terms of observables. The task to construct observables is then disentangled from perturbation theory, thus allowing to unambiguously develop perturbation theory to arbitrary orders. In this first paper of the series we outline and showcase this approach for spherical symmetry and second order in the perturbations for Einstein–Klein–Gordon–Maxwell theory. Details and generalizations to other matter and symmetry and higher orders will appear in subsequent companion papers. [ABSTRACT FROM AUTHOR]

Firstly, it is possible to consider a similar problem of admissible electromagnetic fields classification for the Dirac-Fock equation, since non-commutative integration is also applicable to this equation. This Special issue contains top-tier physics-related and mathematical research, among other topics, written by scholars who are well-known in their field. Second, the results can be used to obtain exact self-consistent solutions in the General Theory of Relativity, in the scalar-tensor theory of gravity, for the Vaidya problem, as well as in the integration of field equations in other gravitational theories. [Extracted from the article]

Linear confinement with Casimir scaling of the string tension in confining gauge theories is a consequence of a certain property of the Polyakov loop related to random matrices. This mechanism does not depend on the details of the theories (neither the gauge group nor dimensions) and explains approximate Casimir scaling below string-breaking length. In this paper, we study 3d SU(2) pure Yang-Mills theory numerically and find the same random-matrix behavior for rectangular Wilson loops. We conjecture that this is a universal feature of strongly coupled confining gauge theories. [ABSTRACT FROM AUTHOR]

We find a general formula for the two-loop renormalization counterterms of a scalar quantum field theory with interactions containing up to two derivatives, extending 't Hooft's one-loop result. The method can also be used for theories with higher derivative interactions, as long as the terms in the Lagrangian have at most one derivative acting on each field. We show that diagrams with factorizable topologies do not contribute to the renormalization group equations. The results in this paper will be combined with the geometric method in a subsequent paper to obtain the counterterms and renormalization group equations for the scalar sector of effective field theories (EFT) to two-loop order. [ABSTRACT FROM AUTHOR]

This paper discusses the relationship between Mock-Lie algebras, Lie algebras, and Jordan algebras. It highlights the importance of the Yang-Baxter equation and symplectic forms in the study of integrable systems, quantum groups, and topological quantum field theory. The paper also proposes studying the admissible associative Yang-Baxter equation in algebras and characterizing Q-Admissible Solutions of the Associative Yang-Baxter Equation in Rota-Baxter Algebras. Finally, it discusses the interplay of coalgebra, r-matrix, and pseudo-Euclidean forms in the context of Jordan algebras and its applications in quantum groups and integrable systems. [ABSTRACT FROM AUTHOR]

This article discusses the measurement of complexity in large complex projects (LCPs) using concepts from quantum physics and relativistic theory. It introduces the concept of Quantum Project Management, which draws analogies from quantum phenomena to provide project managers with a fresh perspective on navigating the complexities of LCPs. The article explores metrics such as entanglement entropy, quantum circuit complexity, computational complexity, quantum Kolmogorov complexity, and quantum Fisher information to quantify complexity in LCPs. It emphasizes the importance of understanding complexity in both quantum computing and LCP to guide decision-making and resource allocation. Overall, Quantum Project Management offers a new perspective on managing LCPs and emphasizes the need to embrace complexity and uncertainty in project management. [Extracted from the article]

The goal of this paper is to present a spectral theory of advanced photon-counting computerized X-ray tomography, which is a promising microelectronical semiconductor wafer X-ray technique on the verge of becoming clinically feasible and has the potential to dramatically alter the clinical application of computer-aided medical diagnosis in the upcoming decades. In analogy to the deep fact that any real division algebra has dimension 1, 2, 4 or 8, the isogeneous third Galois cohomological, mirror symmetrical approach to high spatial resolution spectral photon-counting computerized tomography establishes that the exceptional Lie group Spin (8 , R) is the only one of the spin group spectrum { Spin (n , R) ∣ n ≥ 1 } to admit a triality automorphism. It is the exceptional phenomenon of triality which is able to produce by the spin representation theory of the exceptional Lie group of octonions O the spectral shaped digital signals of spectral photon-counting computerized X-ray tomography. Similarly to spin echo magnetic resonance tomography, the mathematical approach to spectral high performance computerized tomography is based on the isogeneously invariant, projectively weighted, symplectic coadjoint orbit picture Lie (N) ∗ / CoAd (N) of the real 3-dimensional Heisenberg unipotent Lie group N of type GL (3 , R) , and its solvable diamond toric Lie group extension. [ABSTRACT FROM AUTHOR]

This article discusses the importance of studying the history of physics and its relevance to contemporary physics. It emphasizes the need for historical analysis to be independent and not influenced by current research agendas or biases. The article also describes the concept of "History for Physics," which aims to bridge contemporary physics topics with their historical context. The authors organized symposia and published a special issue on this theme, featuring tandem articles written by both physicists and historians of physics. The article concludes by highlighting the positive response from physicists and the potential for further collaboration between physicists and historians in studying the history of physics. Additionally, the article mentions the challenges faced by tandems in completing their papers, resulting in multiple deadline extensions, but expresses excitement and pride in featuring six tandem papers in the special issue. [Extracted from the article]

Random tensor models have applications in a variety of fields, such as quantum gravity, quantum information theory, mathematics of modern technologies, etc. and studying their statistical properties, e.g. tensor eigenvalue/vector distributions, is interesting and useful. Recently some tensor eigenvalue/vector distributions have been computed by expressing them as partition functions of 0D quantum field theories. In this paper, using this method, we compute three cases of complex eigenvalue/vector distributions of symmetric order-three random tensors, where the three cases can be characterized by the Lie-group invariances, |$O(N,\mathbb {R})$|⁠ , |$O(N,\mathbb {C})$|⁠ , and |$U(N,\mathbb {C})$|⁠ , respectively. Exact closed-form expressions of the distributions are obtained by computing partition functions of four-fermi theories, where the last case is of the "signed" distribution, which counts the distribution with a sign factor coming from a Hessian matrix. As an application, we compute the injective norm of the complex symmetric order-three random tensor in the large- N limit by computing the edge of the last signed distribution, obtaining agreement with an earlier numerical result in the literature. [ABSTRACT FROM AUTHOR]

We extend the formula for correlation functions of free scalar field theories and Dirac field theories in terms of quantum |$A_{\infty }$| algebras presented in arXiv:2305.11634 to general scalar-Dirac systems. We obtain the result that the same formula as in the previous paper holds in this case. We show that correlation functions from our formula satisfy the Schwinger–Dyson equations. We therefore confirm that correlation functions from our formula express correlation functions from the ordinary approach of quantum field theory. [ABSTRACT FROM AUTHOR]