Thermal quantum field theory Khanna, Faqir C; Khanna, Faqir C; Malbouisson, Adolfo P. C ...
2009., 2009, 2009-02-06
eBook
This monograph presents recent developments in quantum field theory at finite temperature. By using Lie groups, ideas from thermal theory are considered with concepts of symmetry, allowing for ...applications not only to quantum field theory but also to transport theory, quantum optics and statistical mechanics. This includes an analysis of geometrical and topological aspects of spatially confined systems with applications to the Casimir effect, superconductivity and phase transitions. Finally, some developments in open systems are also considered. The book provides a unified picture of the fundamental aspects in thermal quantum field theory and their applications, and is important to the field as a result, since it combines several diverse ideas that lead to a better understanding of different areas of physics.
The Dirac field, spin 1/2 particles, is investigated in phase space. The Dirac propagator is defined. The Thermo Field Dynamics (TFD) formalism is used to introduce finite temperature. The ...energy-momentum tensor is calculated at finite temperature. The Stefan-Boltzmann law is established, and the Casimir effect is calculated for the Dirac field in phase space at zero and finite temperature. A comparative analysis with these results in standard quantum mechanics space is realized.
The standard representation of
c
∗
-algebra is used to describe fields in compactified space–time dimensions characterized by topologies of the type
Γ
D
d
=
(
S
1
)
d
×
M
D
−
d
. The modular operator ...is generalized to introduce representations of isometry groups. The Poincaré symmetry is analyzed and then we construct the modular representation by using linear transformations in the field modes, similar to the Bogoliubov transformation. This provides a mechanism for compactification of the Minkowski space–time, which follows as a generalization of the Fourier integral representation of the propagator at finite temperature. An important result is that the 2×2 representation of the real-time formalism is not needed. The end result on calculating observables is described as a condensate in the ground state. We initially analyze the free Klein–Gordon and Dirac fields, and then formulate non-abelian gauge theories in
Γ
D
d
. Using the
S
-matrix, the decay of particles is calculated in order to show the effect of the compactification.
►
C
∗
-algebra is used to describe fields in compactified space-time dimensions. ► The space–time is characterized by toroidal topologies. ► Representations of the Poincaré group are studied by using the modular operator. ► We derive non-abelian gauge theories in compactified regions of space–time. ► We show the compactification effect in the decay of particles using the
S
-matrix.
Gravitons are described by the propagator in teleparallel gravity in nearly flat space-time. Finite temperature is introduced by using Thermofield Dynamics formalism. The gravitational Casimir effect ...and Stefan-Boltzmann law are calculated as a function of temperature. Then an equation of state for gravitons is determined.
Weyl gravitoelectromagnetism Ramos, J.; de Montigny, M.; Khanna, F. C.
General relativity and gravitation,
07/2018, Letnik:
50, Številka:
7
Journal Article
Recenzirano
We study the gauge transformation in the context of gravitoelectromagnetism and introduce a new expression for the phase factor. Using these concepts and with the principle of local gauge invariance ...applied to physical theories, a formal derivation of gravitoelectromagnetism is obtained.
Zeeman Effect in Phase Space Paiva, R. A. S.; Amorim, R. G. G.; Ulhoa, S. C. ...
Advances in high energy physics,
2020, Letnik:
2020
Journal Article
Recenzirano
Odprti dostop
The two-dimensional hydrogen atom in an external magnetic field is considered in the context of phase space. Using the solution of the Schrödinger equation in phase space, the Wigner function related ...to the Zeeman effect is calculated. For this purpose, the Bohlin mapping is used to transform the Coulomb potential into a harmonic oscillator problem. Then, it is possible to solve the Schrödinger equation easier by using the perturbation theory. The negativity parameter for this system is realised.
The Abelian and non-Abelian gauge symmetries extended to the gravitational interaction are explored by following the gravitoelectromagnetism approach. Then a correspondence with the weak-field ...approximation of gravity up to second order is developed.
•Abelian and non-Abelian gauge symmetries applied to the gravitational interaction.•Analogy between Abelian and non-Abelian gravitoelectromagnetism and the weak-field.•Gravitoelectromagnetic concepts similar to those of the Yang–Mills theory.•Yang–Mills-like equations are obtained for non-Abelian Weyl gravitoelectromagnetism.•A new matrix for the gravitoelectromagnetic potential Aμν is obtained.
Small violation of Lorentz and CPT symmetries may emerge in models unifying gravity with other forces of nature. An extension of the standard model with all possible terms that violate Lorentz and ...CPT symmetries are included. Here a CPT-even non-minimal coupling term is added to the covariant derivative. This leads to a new interaction term that breaks the Lorentz symmetry. Our main objective is to calculate the cross section for the e−+e+→μ−+μ+ scattering in order to investigate any violation of Lorentz and/or CPT symmetry at finite temperature. Thermo Field Dynamics formalism is used to consider finite temperature effects.
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