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We develop a systematic DLCQ perturbation theory and show that DLCQ S-matrix does not have a covariant continuum limit for processes with p⁺=0 exchange. This implies that the role of the zero mode is more subtle than ever considered in DLCQ and hence must also be treated with great care in nonperturbative approach. We also make a brief comment on DLCQ in string theory.

The possibility of parity violation through space–time torsion has been explored in a scenario containing fields with different spins. Taking the Kalb–Ramond (KR) field as the source of torsion, an explicitly parity violating U(1) _EM gauge-invariant theory has been constructed by extending the KR field with a Chern–Simons term.

We demonstrate that the Hamiltonian structure and the integrability of a system of evolution equations can be formulated in terms of a classical field theory using BRST and anti-BRST symmetries. We derive the field theory action and explicitly generate the integrable hierarchy associated to a bi-Hamiltonian system based on cohomological arguments and gauge-fixing deformations.

We consider the generic non-anticommutative model of chiral–antichiral superfields on superspace. The model is formulated in terms of an arbitrary Kählerian potential, chiral and antichiral superpotentials and can include the non-anticommutative supersymmetric sigma-model as a partial case. We study a component structure of the model and derive the component Lagrangian in an explicit form with all auxiliary fields contributions. We show that the infinite series in the classical action for generic non-anticommutative model of chiral–antichiral superfields in D = 4 dimensions can be resumed in a compact expression which can be written as a deformation of standard Zumino's Lagrangian and chiral superpotential. Problem of eliminating the auxiliary fields in the generic model is discussed and the first perturbative correction to the effective scalar potential is obtained.

We study the behavior of the renormalized sextic coupling at the intermediate and strong coupling regime for the φ⁴ theory defined in d = 2 dimensions. We found a good agreement with the results obtained by the field-theoretical renormalization-group in the Ising limit. In this work we use the lattice regularization method.

We have introduced the Cornwall–Jackiw–Tomboulis (CJT) resummation scheme in studying nuclear matter. Based on the CJT formalism and using Walecka model, we have derived a set of coupled Dyson equations of nucleons and mesons. Neglecting the medium effects of the mesons, the usual mean field theory (MFT) results can be obtained. The beyond MFT calculations have been performed by thermodynamic consistently determining the meson effective masses and solving the coupled gap equations for nucleons and mesons together. The numerical results for the nucleon and meson effective masses at finite temperature and chemical potential in nuclear matter are discussed.

In this paper we present Darboux transformation for the principal chiral and WZW models in two dimensions and construct multi-soliton solutions in terms of quasideterminants. We also establish the Darboux transformation on the holomorphic conserved currents of the WZW model and expressed them in terms of the quasideterminant. We discuss the model based on the Lie group SU(n) and obtain explicit soliton solutions for the SU(2) model.

A nonassociative Groenewold–Moyal (GM) plane is constructed using quaternion-valued function algebras. The symmetrized multiparticle states, the scalar product, the annihilation/creation algebra and the formulation in terms of a Hopf algebra are also developed. Nonassociative quantum algebras in terms of position and momentum operators are given as the simplest examples of a framework whose applications may involve string theory and nonlinear quantum field theory.

One of the disadvantages of the Hamiltonian formulation is that Lorentz invariance is not manifest in the former. Given a Hamiltonian, there is no simple way to check whether it is relativistic or not. One would either have to solve for the equations of motion or calculate the Poisson brackets of the Noether charges to perform such a check. In this paper we show that, for a class of Hamiltonians, it is possible to check Lorentz invariance directly from the Hamiltonian. Our work is particularly useful for theories where the other methods may not be readily available.

We examine Podolsky’s electrodynamics, which is non-invariant under the usual duality transformation. We deduce a generalization of Hodge’s star duality, which leads to a dual gauge field and restores to a certain extent the dual symmetry. The model becomes fully dual symmetric asymptotically, when it reduces to the Maxwell theory. We argue that this strict dual symmetry directly implies the existence of the basic invariants of the electromagnetic fields.

Novel bound states are obtained for manifolds with singular potentials. These singular potentials require proper boundary conditions across boundaries. The number of bound states matches nicely with what we would expect for black holes. Also they serve to model membrane mechanism for the black hole horizons in simpler contexts. The singular potentials can also mimic expanding boundaries elegantly, thereby obtaining appropriately tuned radiation rates.

A geometrical approach to the covariant formulation of the dynamics of relativistic systems is introduced. A realization of Peierls brackets by means of a bivector field over the space of solutions of the Euler–Lagrange equations of a variational principle is presented. The method is illustrated with some relevant examples.

We show that the space of observables of test particles has a natural Jacobi structure which is manifestly invariant under the action of the Poincaré group. Poisson algebras may be obtained by imposing further requirements. A generalization of Peierls procedure is used to extend this Jacobi bracket to the space of time-like geodesics on Minkowski spacetime.

Cosmological solutions for covariant canonical gauge theories of gravity are presented. The underlying covariant canonical transformation framework invokes a dynamical spacetime Hamiltonian consisting of the Einstein–Hilbert term plus a quadratic Riemann tensor invariant with a fundamental dimensionless coupling constant $g_1$. A typical time scale related to this constant, $\tau =\sqrt{8\pi G{g}_1}$, is characteristic for the type of cosmological solutions: for $t\ll \tau$, the quadratic term is dominant, the energy–momentum tensor of matter is not covariantly conserved, and we observe modified dynamics of matter and spacetime. On the other hand, for $t\gg \tau$, the Einstein term dominates and the solution converges to classical cosmology. This is analyzed for different types of matter and dark energy with a constant equation of state. While for a radiation-dominated universe solution, the cosmology does not change, we find for a dark energy universe the well-known de-Sitter space. However, we also identify a special bouncing solution (for $k=0$) which for large times approaches the de-Sitter space again. For a dust-dominated universe (with no pressure), deviations are seen only in the early epoch. In late epoch, the solution asymptotically behaves as the standard dust solution.

We analyze, from a canonical quantum field theory (QFT) perspective, the problem of one-dimensional particles with three-body attractive interactions, which was recently shown to exhibit a scale anomaly identical to that observed in two-dimensional (2D) systems with two-body interactions. We study in detail the properties of the scattering amplitude including both bound and scattering states, using cutoff and dimensional regularization, and clarify the connection between the scale anomaly derived from thermodynamics to the nonvanishing non-relativistic trace of the energy–momentum tensor.

The analysis of the covariant brackets on the space of functions on the solutions to a variational problem in the framework of contact geometry initiated in the companion letter${}^{19}$ is extended to the case of the multisymplectic formulation of the free Klein–Gordon theory and of the free Schrödinger equation.

A novel reduction procedure for covariant classical field theories, reflecting the generalized symplectic reduction theory of Hamiltonian systems, is presented. The departure point of this reduction procedure consists in the choice of a submanifold of the manifold of solutions of the equations describing a field theory. Then, the covariance of the geometrical objects involved, will allow to define equations of motion on a reduced space. The computation of the canonical geometrical structure is performed neatly by using the geometrical framework provided by the multisymplectic description of covariant field theories. The procedure is illustrated by reducing the D’Alembert theory on a five-dimensional Minkowski space-time to a massive Klein–Gordon theory in four dimensions and, more interestingly, to the Schrödinger equation in 3 + 1 dimensions.

Dark energy is the largest fraction of the energy density of our universe — yet it remains one of the enduring enigmas of our times. Here we show that dark energy can be used to solve 2 tantalizing mysteries of the observable universe. We build on existing models of dark energy linked to neutrino masses. In these models, dark energy can undergo phase transitions and form black holes. Here we look at the implications of the family structure of neutrinos for the phase transitions in dark energy and associated peaks in black hole formation. It has been previously shown that one of these peaks in black hole formation is associated with the observed peak in quasar formation at redshifts $z\sim 2.5$. Here, we predict that there will also be an earlier peak in the dark energy black holes at high redshifts $z\sim 18$. These dark energy black holes formed at high redshifts are Intermediate Mass Black Holes (IMBHs). These dark energy black holes at large redshift can help explain both the EDGES observations and the observations of large Supermassive Black Holes (SMBHs) at redshifts of 7 or larger. This work directs us to actively look for these dark energy black holes at these high redshifts as predicted here through targeted searches for these black holes at the redshifts $z$ near 18. There is a slight dependence of the location of the peak on the lightest neutrino mass. This may enable a measurement of the lightest neutrino mass — something which has eluded us so far. Finding these dark energy black holes of Intermediate Mass should be within the reach of upcoming observations — particularly with the James Webb Space Telescope — but perhaps also through the use of other innovative techniques focusing specifically on the redshifts $z$ around 18.

In this work, we propose a parity-invariant Maxwell–Chern–Simons $\mathrm{\text{U}}(1)\times \mathrm{\text{U}}(1)$ model coupled with two charged scalar fields in $2+1$ dimensions, and show that it admits finite-energy topological vortices. We describe the main features of the model and find explicit numerical solutions for the equations of motion, considering different sets of parameters and analyzing some interesting particular regimes. We remark that the structure of the theory follows naturally from the requirement of parity invariance, a symmetry that is rarely envisaged in the context of Chern–Simons theories. Another distinctive aspect is that the vortices found here are characterized by two integer numbers.

A non-Abelian theory of fermions interacting with gauge bosons, the constrained system, is studied. The equations of motion for a singular system are obtained as total differential equations in many variables. The integrability conditions are investigated, and the set of equations of motion is integrable. The Senjanovic and the canonical methods are used to quantize the system, and the integration is taken over the canonical phase space coordinates.