International Journal of Modern Physics A

In this note we discuss the question of gauge invariance in the presence of a minimal length. This contribution is prepared for the celebration of the 60th anniversary of the Yang–Mills theory.

Respecting that any consistent quantum field theory in curved space–time must include black hole radiation, in this paper, we examine the Krein–Gupta–Bleuler (KGB) formalism as an inevitable quantization scheme in order to follow the guideline of the covariance of minimally coupled massless scalar field and linear gravity on de Sitter (dS) background in the sense of Wightman–Gärding approach, by investigating thermodynamical aspects of black holes. The formalism is interestingly free of pathological large distance behavior. In this construction, also, no infinite term appears in the calculation of expectation values of the energy–momentum tensor (we have an automatic and covariant renormalization) which results in the vacuum energy of the free field to vanish. However, the existence of an effective potential barrier, intrinsically created by black holes gravitational field, gives a Casimir-type contribution to the vacuum expectation value of the energy–momentum tensor. On this basis, by evaluating the Casimir energy–momentum tensor for a conformally coupled massless scalar field in the vicinity of a nonrotating black hole event horizon through the KGB quantization, in this work, we explicitly prove that the hole produces black-body radiation which its temperature exactly coincides with the result obtained by Hawking for black hole radiation.

Comparative analysis of the interplay of hadron and Coulomb interactions in $p{p}^{\pm }$ scattering amplitudes is performed in a broad energy interval, $\sqrt{s}=1\text{–}10^6\mathrm{\text{TeV}}$, for two extreme cases: for the asymptotic interactions of hadrons in black disk and resonant disk modes. The interactions are discussed in terms of the $K$-matrix function technique. In the asymptotic regime, the real part of the hadronic amplitude is concentrated in both cases on the boundary of the disks in the impact parameter space but the LHC energy region is not asymptotic for the resonant disk mode that lead to a specific interplay of hadronic and Coulombic amplitudes. For the $pp$ scattering at $\sqrt{s}\sim 10\mathrm{\text{TeV}}$ an interplay of the hadron and Coulomb interactions in the resonant disk modes is realized in a shoulder in $d{\sigma }_{\mathrm{\text{el}}}/d{q}^2$ at $q^2\sim 0.0025\text{–}0.0075{\mathrm{\text{GeV}}}^2$. The absence of such a shoulder in the data at 8 TeV can be considered as an argument against the resonant disk mode.

We develop a new version of the superfield Hamiltonian quantization. The main new feature is that the BRST-BFV charge and the gauge fixing Fermion are introduced on equal footing within the sigma model approach, which provides for the actual use of the quantum/derived antibrackets. We study in detail the generating equations for the quantum antibrackets and their primed counterparts. We discuss the finite quantum anticanonical transformations generated by the quantum antibracket.

We study the thermodynamic properties of the Bose–Einstein condensate (BEC) in the context of the quantum field theory with noncommutative target space. Our main goal is to investigate in which temperature and/or energy regimes the noncommutativity can characterize some influence on the BEC properties described by a relativistic massive noncommutative boson gas. The noncommutativity parameters play a key role in the modified dispersion relations of the noncommutative fields, leading to a new phenomenology. We have obtained the condensate fraction, internal energy, pressure and specific heat of the system and taken ultrarelativistic (UR) and nonrelativistic (NR) limits. The noncommutative effects on the thermodynamic properties of the system are discussed. We found that there appear interesting signatures around the critical temperature.

A model of nonlinear electromagnetic fields with a dimensional parameter $\beta$ is proposed. From PVLAS experiment the bound on the parameter $\beta$ was obtained. Electromagnetic fields are coupled with the gravitation field and we show that the universe accelerates due to nonlinear electromagnetic fields. The magnetic universe is considered and the stochastic magnetic field is a background. After inflation the universe decelerates and approaches to the radiation era. The range of the scale factor, when the causality of the model and a classical stability take place, was obtained. The spectral index, the tensor-to-scalar ratio, and the running of the spectral index were estimated which are in approximate agreement with the Planck, WMAP, and BICEP2 data.

There is a growing interest for the search of new light gauge bosons. The small mass of a new boson can turn various kinds of low-energy experiments to a new discovery machine, depending on their couplings to the Standard Model particles. It is important to understand the properties of each type of gauge boson and their current constraints for a given mass. While the dark photon (which couples to the electric charges) and the $U{(1)}_{B-L}$ gauge boson have been well studied in an extensive mass range, the $U{(1)}_L$ gauge boson has not been fully investigated yet. We consider the gauge boson of the $U{(1)}_L$ in a wide mass range $m_{Z^{\prime }}\approx 0\text{–}10^{12}\mathrm{\text{eV}}$ and investigate the constraints on its coupling from various experiments, discussing the similarities and differences from the dark photon and the $U{(1)}_{B-L}$ gauge boson.

We investigate conserved charges in the low-energy effective field theory describing heterotic string theory. Starting with a general Lagrangian that consists of a metric, a scalar field, a vector gauge field, together with a two-form potential, we derive off-shell Noether potentials of the Lagrangian and generalize the Abbott–Deser–Tekin (ADT) formalism to the off-shell level by establishing one-to-one correspondence between the ADT potential and the off-shell Noether potential. It is proved that the off-shell generalized ADT formalism is conformally invariant. Then, we apply the formulation to compute mass and angular momentum of the four-dimensional Kerr–Sen black hole and the five-dimensional rotating charged black string in the string frame without a necessity to transform the metrics into the Einstein frame.

By considering a general Abelian chiral gauge theory, we investigate the behavior of anomalous Ward–Takahashi (WT) identities concerning their prediction for the usual relationship between the vertex and two-point fermion functions. Using gauge anomaly vanishing results, we show that the usual (in the nonanomalous case) WT identity connecting the vertex and two-point fermion 1PI functions is modified for Abelian chiral gauge theories. The modification, however, implies a relation between fermion and charge renormalization constants that can be important in a future study of renormalization of such theories.

We present the Higgs mechanism in the context of the EW-scale ${\nu }_R$ model in which electroweak symmetry is dynamically broken by condensates of mirror quark and right-handed neutrino through the exchange of one fundamental Higgs doublet and one fundamental Higgs triplet, respectively. The formation of these condensates is dynamically investigated by using the Schwinger–Dyson approach. The occurrence of these condensates will give rise to the rich Higgs spectrum. In addition, the VEVs of Higgs fields is also discussed in this dynamical phenomenon.