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.
Gravitons are described by the propagator in Teleparallel gravity in nearly flat space-time. Finite temperature is introduced by using Thermo Field 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.
In this paper we use the scalar field constructed in phase space to analyze the analogous Stefan-Boltzman law and Casimir effect both of them at finite temperature. The temperature is introduced by Thermo Field Dynamics (TFD) and the quantities are analyzed once projected in the coordinates space.
A spatially flat Friedmann-Robertson-Walker background with a general scale factor is considered. In this space-time, the energy-momentum tensor of the scalar field with a general curvature coupling parameter is obtained. Using the Thermo Field Dynamics (TFD) formalism the Stefan-Boltzmann law and the Casimir effect at finite temperature are calculated. The Casimir effect at zero temperature is also considered. The expansion of the universe changes these effects. A discussion of these modifications is presented.
The standard model and general relativity are local Lorentz invariants. However it is possible that at Planck scale there may be a breakdown of Lorentz symmetry. Models with Lorentz violation are constructed using Standard Model Extension (SME). Here gravitational sector of the SME is considered to analyze the Lorentz violation in Gravitoelectromagnetism (GEM). Using the energy-momentum tensor, the Stefan-Boltzmann law and Casimir effect are calculated at finite temperature to ascertain the level of local Lorentz violation. Thermo Field Dynamics (TFD) formalism is used to introduce temperature…
A non-Abelian gauge theory describes the strong interactions among particles with the commutator of generators are non-zero. An $SU(3)$ gauge theory describes the interactions that lead to nuclear forces among particles. The Lagrangian density refers to fermions with colour and flavour and the gauge field quanta implying gluons. The gauge theory is treated at finite temperature using the Thermo Field Dynamics (TFD). Using self interaction of gluons the Stefan-Boltzmann law and the Casimir effect are calculated at finite temperature. An appendix is attached to give a response of a massless quar…
In this work we study Podolsky electromagnetism in thermodynamic equilibrium. We show that a Podolsky mass-dependent modification to the Stefan-Boltzmann law is induced and we use experimental data to limit the possible values for this free parameter.
This paper deals with quantum field theory in curved space-time using the Thermo Field Dynamics. The scalar field is coupled to the Schwarzschild space time and then thermalised. The Stefan-Boltzmann law is established at finite temperature and the entropy of the field is calculated. Then the Casimir energy and pressure are obtained at zero and finite temperature.
This paper generalizes the Stefan-Boltzmann law to include massive photons. A crucial ingredient to obtain the correct formula for the radiance is to realize that a massive photon does not travel at the speed of (massless) light. It follows that, contrary to what could be expected, the radiance is not proportional to the energy density times the speed of light.
The Galilean covariance, formulated in 5-dimensions space, describes the non-relativistic physics in a way similar to quantum field theory. Using a non-relativistic approach the Stefan-Boltzmann law and the Casimir effect at finite temperature for a particle with spin zero and $1/2$ are calculated. The Thermo Field Dynamics is used to calculate the temperature effect.
In the celebrated Unruh effect, we learn that a uniformly accelerating detector in a Minkowski vacuum spacetime registers a constant temperature. Building on prior work, we present a technique based on derivative couplings of the two-point Wightman function and the Hadamard renormalization procedure to define an instantaneous temperature for a massive scalar field, non-minimally coupled to gravity. We find the temperature contains local contributions from the acceleration of the detector, the curvature of spacetime, and the renormalized stress-energy tensor of the field. Our result, which can …
In this paper, a massless scalar field coupled to gravity is considered. Then the Casimir effect at finite temperature is calculated. Such development is carried out in the Thermo Field Dynamics formalism. This approach presents a topological structure that allows for investigating the effects of temperature and the size effect in a similar way. These effects are calculated considering Gödel-type solutions as a gravitational background. The Stefan-Boltzmann law and its consistency are analyzed for both causal and non-causal Gödel-type regions. In this space-time and for any region, the Casimir…
Where does Hawking radiation originate? A common picture is that it arises from excitations very near or at the horizon, and this viewpoint has supported the "firewall" argument and arguments for a key role for the UV-dependent entanglement entropy in describing the quantum mechanics of black holes. However, closer investigation of both the total emission rate and the stress tensor of Hawking radiation supports the statement that its source is a near-horizon quantum region, or "atmosphere," whose radial extent is set by the horizon radius scale. This is potentially important, since Hawking rad…
Recently a great deal of interest in field theories formulated in a Lorentz violating framework has been developed. Here the Very Special Relativity (VSR) is considered. The main aspect in the VSR proposal is that laws of physics are invariant under the subgroups of the Poincaré group preserving the basic elements of special relativity. An important point is that the photon acquires a mass. In this context, the energy-momentum tensor for the electromagnetic field is calculated. From this, the Stefan-Boltzmann law and Casimir effect at finite temperature in VSR are obtained. The effects of temp…
It has recently been suggested [S. B. Giddings, Phys. Lett. B {\bf 754}, 39 (2016)] that the Hawking black-hole radiation spectrum originates from an effective quantum "atmosphere" which extends well outside the black-hole horizon. In particular, comparing the Hawking radiation power of a $(3+1)$-dimensional Schwarzschild black hole of horizon radius $r_{\text{H}}$ with the familiar Stefan-Boltzmann radiation power of a $(3+1)$-dimensional flat space perfect blackbody emitter, Giddings concluded that the source of the Hawking semi-classical black-hole radiation is a quantum region outside the …
The blackbody radiation in a box L^3 with periodic boundary conditions in thermal equilibrium at a temperature T is affected by finite-size effects. These bring about modifications of the thermodynamic functions which can be expressed in a closed form in terms of the dimensionless parameter LT. For instance, when LT~4 - corresponding to the value where the most reliable SU(N) gauge lattice simulations have been performed above the deconfining temperature T_c - the deviation of the free energy density from its thermodynamic limit is about 5%. This may account for almost half of the pressure def…
In the footsteps of our previous work \cite{RamatonBoschi} we generalize the Stefan-Boltzmann and Wien's displacement laws for the $ \textrm{AdS}_5 \times {\cal S}^5 $ spacetime, the background of the AdS/CFT correspondence foremost realization. Our results take into account the $ \textrm{AdS}_5 \times {\cal S}^5 $ full dimensionality in the electromagnetic field $A^μ$ wave equation, which yields the higher-dimensional blackbody characteristic features suggested in literature. In particular, the total radiated power and the spectral radiancy match the original Stefan-Boltzmann and Wien's displ…
In warm inflation scenarios, radiation always exists, so that the radiation energy density is also assumed to be finite when inflation starts. To find out the origin of the non-vanishing initial radiation energy density, we revisit thermodynamic analysis for a warm inflation model and then derive an effective Stefan-Boltzmann law which is commensurate with the temperature-dependent effective potential by taking into account the non-vanishing trace of the total energy-momentum tensors. The effective Stefan-Boltzmann law shows that the zero energy density for radiation at the Grand Unification e…
We consider the Casimir force acting on a $d$-dimensional rectangular piston due to massless scalar field with periodic, Dirichlet and Neumann boundary conditions and electromagnetic field with perfect electric conductor and perfect magnetic conductor boundary conditions. It is verified analytically that at any temperature, the Casimir force acting on the piston is always an attractive force pulling the piston towards the interior region, and the magnitude of the force gets larger as the separation $a$ gets smaller. Explicit exact expressions for the Casimir force for small and large plate sep…
In this work, we examine the finite temperature properties of the CPT-even and Lorentz-invariance-violating (LIV) electrodynamics of the standard model extension, represented by the term $W_{ανρϕ}F^{αν}F^{ρϕ}$. We begin analyzing the hamiltonian structure following the Dirac's procedure for constrained systems and construct a well-defined and gauge invariant partition function in the functional integral formalism. Next, we specialize for the non-birefringent coefficients of the tensor $W_{ανρϕ}$. In the sequel, the partition function is explicitly carried out for the parity-even sector of the …
The Yang-Mills-aether theory is considered. Implications of the non-abelian aether-like term, which introduces violation of Lorentz symmetry, is investigated in a thermal quantum field theory. The Thermofield Dynamics formalism is used to introduce the temperature effects and spatial compactification. As a consequence, corrections due to the non-abelian aether term are calculated for the non-abelian Stefan-Boltzmann law and for the non-abelian Casimir energy and pressure at zero and finite temperature.
A famous example of gauge/gravity duality is the result that the entropy density of strongly coupled ${\cal N}=4$ SYM in four dimensions for large N is exactly 3/4 of the Stefan-Boltzmann limit. In this work, I revisit the massless O(N) model in 2+1 dimensions, which is analytically solvable at finite temperature $T$ for all couplings $λ$ in the large N limit. I find that the entropy density monotonically decreases from the Stefan-Boltzmann limit at $λ=0$ to exactly 4/5 of the Stefan-Boltzmann limit at $λ=\infty$. Calculating the retarded energy-momentum tensor correlator in the scalar channel…
Studies about a formal analogy between the gravitational and the electromagnetic fields lead to the notion of Gravitoelectromagnetism (GEM) to describe gravitation. In fact, the GEM equations correspond to the weak field approximation of gravitation field. Here a non-abelian extension of the GEM theory is considered. Using the Thermo Field Dynamics (TFD) formalism to introduce temperature effects some interesting physical phenomena are investigated. The non-abelian GEM Stefan-Boltzmann law and the Casimir effect at zero and finite temperature for this non-abelian field are calculated.
Higher-abelian gauge theories associated with Cheeger-Simons differential characters are studied on compact manifolds without boundary. The paper consists of two parts: First the functional integral formulation based on zeta function regularization is revisited and extended in order to provide a general framework for further applications. A field theoretical model - called extended higher-abelian Maxwell theory - is introduced, which is a higher-abelian version of Maxwell theory of electromagnetism extended by a particular topological action. This action is parametrized by two non-dynamical ha…
The conventional Tolman temperature based on the assumption of the traceless condition of energy-momentum tensor for matter fields is infinite at the horizon if Hawking radiation is involved. However, we note that the temperature associated with Hawking radiation is of relevance to the trace anomaly, which means that the traceless condition should be released. So, a trace anomaly-induced Stefan-Boltzmann law is newly derived by employing the first law of thermodynamics and the property of the temperature independence of the trace anomaly. Then, the Tolman temperature is quantum-mechanically ge…
The Thermo Field Dynamics (TFD) formalism is used to investigate the regular black holes at finite temperature. Using the Teleparalelism Equivalent to General Relativity (TEGR) the gravitational Stefan-Boltzmann law and the gravitational Casimir effect at zero and finite temperature are calculated. In addition, the first law of thermodynamics is considered. Then the gravitational entropy and the temperature of the event horizon of a class of regular black holes are determined.
We consider a relativistic strongly interacting Bose gas. The interaction is manifested in the off-shellness of the equilibrium distribution. The equation of state that we obtain for such a gas has the properties of a realistic equation of state of strongly interacting matter, i.e., at low temperature it agrees with the one suggested by Shuryak for hadronic matter, while at high temperature it represents the equation of state of an ideal ultrarelativistic Stefan-Boltzmann gas, implying a phase transition to an effectively weakly interacting phase.
By invoking inverse temperature as a van Kampen-Isreal future-directed timelike 4-vector, this paper derives the Relativistic Blackbody Spectrum, the Relativistic Wien's Displacement Law, and the Relativistic Stefan-Boltzmann Law in inertial and non-inertial reference frames.
We compute the phase and the modulus of an energy- and pressure-free, composite, adjoint, and inert field $ϕ$ in an SU(2) Yang-Mills theory at large temperatures. This field is physically relevant in describing part of the ground-state structure and the quasiparticle masses of excitations. The field $ϕ$ possesses nontrivial $S^1$-winding on the group manifold $S^3$. Even at asymptotically high temperatures, where the theory reaches its Stefan-Boltzmann limit, the field $ϕ$, though strongly power-suppressed, is conceptually relevant: its presence resolves the infrared problem of thermal perturb…
This work examines the finite temperature properties of the CPT-even and parity-odd electrodynamics of the standard model extension. We start from the partition function written into the functional integral formalism in Ref. \cite{Finite}. After specializing the Lorentz-violating tensor $ W_{ανρφ}$ for the nonbirefringent and parity-odd coefficients, the partition function is explicitly carry out, showing that it is a power of the Maxwell's partition function. Also, it is observed that the LIV coefficients induce an anisotropy in the black body angular energy density distribution. The Planck's…
The Thermofield Dynamics (TFD) formalism is considered. In this context, a Lorentz-breaking scalar field theory is introduced. In contrast to the Matsubara formalism, the best-known approach to introducing the temperature effect, TFD is a real-time formalism and is a topological field theory. While in Matsubara the temperature effects are introduced as a consequence of a compactification of the field in a finite interval on the time axis, in the TFD this effect emerges through a condensed state related to the Bogoliubov transformation. An advantage of the TFD formalism is that different topolo…
We study the finite temperature properties of the Maxwell-Carroll-Field-Jackiw (MCFJ) electrodynamics for a purely spacelike background. Starting from the associated finite temperature partition function, a modified black body spectral distribution is obtained. We thus show that, if the CMB radiation is described by this model, the spectrum presents an anisotropic angular energy density distribution. We show, at leading order, that the Lorentz-breaking contributions for the Planck's radiation law and for the Stefan-Boltzmann's law are nonlinear in frequency and quadratic in temperature, respec…
We analyze the problem of black body radiation in the presence of quantum gravity effects encoded in modified dispersion relations and in a model universe with large extra dimensions. In this context, modified form of Planck distribution, Jeans number, equipartition theorem, spectral energy density, Stefan-Boltzmann law and Wien's law are found and the corresponding results are interpreted. Then, entropy and specific heat of black body radiation are obtained in this setup. Finally, the modified form of Debye law and Dulong-Petit law are investigated in this framework.
Motivated by the recent shocking results from RHIC and LHC that show quark-gluon plasma signatures in small systems, we study a simple model of a massless, noninteracting scalar field confined with Dirichlet boundary conditions. We use this system to investigate the finite size corrections to thermal field theoretically derived quantities compared to the usual Stefan-Boltzmann limit of an ideal gas not confined in any direction. Two equivalent expressions with different numerical convergence properties are found for the free energy in $D$ rectilinear spacetime dimensions with $c\le D-1$ spatia…
We analyze the finite temperature behaviour of massless conformally coupled scalar fields in homogeneous lens spaces $S^3/{\mathbb Z}_p$. High and low temperature expansions are explicitly computed and the behavior of thermodynamic quantities under thermal duality is scrutinized. The analysis of the entropy of the different lens spaces in the high-temperature limit points out the appearance of a topological nonextensive entropy, besides the standard Stefan-Boltzmann extensive term. The remaining terms are exponentially suppressed by the temperature. The topological entropy appears as a sublead…
In this work we generalize the Stefan-Boltzmann and Wien's displacement laws for a $D$-dimensional manifold composed by 4 non-compact dimensions and $D-4$ compact dimensions, $ R^{1,3}$ x $T^{D-4} $. The electromagnetic field is assumed to pervade all compact and non-compact dimensions. In particular, the total radiated power becomes $ R(T) = σ_B T^4 + σ_D (a) \, T^D $, where $a$ is the size of the compact extra dimensions. For $D=10$, predicted from String Theory, and $D=11$, from M-Theory, the outcomes agree with available experimental data for $a$ as high as 2 x $10^{-7}$m.
Supersymmetric renormalization group (RG) flow equations for the effective superpotential of the three-dimensional Wess-Zumino model are derived at zero and non-zero temperature. This model with fermions and bosons interacting via a Yukawa term possesses a supersymmetric analogue of the Wilson-Fisher fixed-point. At zero temperature we determine the phase-transition line in coupling-constant space separating the supersymmetric from the non-supersymmetric phase. At finite temperature we encounter dimensional reduction from 3 to 2 dimensions in the infrared regime. We determine the finite-temper…
From infinite to infinitesimal: Using the Universe as a dataset to probe Casimir corrections to the vacuum energy from fields inhabiting the dark dimension
We apply the concept of reflection-transmission (RT) algebra, originally developed in the context of integrable systems in 1+1 space-time dimensions, to the study of finite temperature quantum field theory with impurities in higher dimensions. We consider a scalar field in $(s+1)+1$ space-time dimensions, interacting with impurities localized on $s$-dimensional hyperplanes, but without self-interaction. We discuss first the case $s=0$ and extend afterwards all results to $s>0$. Constructing the Gibbs state over an appropriate RT algebra, we derive the energy density at finite temperature and e…
Decoherence effects at finite temperature (T) are examined for two manifestly quantum systems: (i) Casimir forces between parallel plates that conduct along different directions, and (ii) a topological Aharonov-Bohm (AB) type force between fluxons in a superconductor. As we illustrate, standard path integral calculations suggest that thermal effects may remove the angular dependence of the Casimir force in case (i) with a decoherence time set by h/(k_{B} T) where h is Plank's constant and k_{B} is the Boltzmann constant. This prediction may be tested. The effect in case (ii) is due a phase shi…
In this work we present the generalization of some thermodynamic properties of the black body radiation (BBR) towards an $n-$dimensional Euclidean space. For this case the Planck function and the Stefan-Boltzmann law have already been given by Landsberg and de Vos and some adjustments by Menon and Agrawal. However, since then no much more has been done on this subject and we believe there are some relevant aspects yet to explore. In addition to the results previously found we calculate the thermodynamic potentials, the efficiency of the Carnot engine, the law for adiabatic processes and the he…
I present a study of the equation of state in quenched QCD, discussing some systematic effects related to the lattice geometry. In particular, I comment on the modification of the Stefan-Boltzmann law for a gas of free gluons in a finite system, and study the impact it might have on numerical results at high temperatures, for the typical parameters of current lattice simulations. Finally, I apply the results of this study to the analysis of data obtained from simulations of SU(N) gauge theories with N>3 colors, in a temperature range up to 3T_c, where infrared effects appear to be under contro…
