Finite Temperature Quantum Field Theory Research Articles

Finite temperature quantum field theory in the functional Schrödinger picture.

We calculate the finite temperature Gaussian effective potential of scalar ${\mathrm{\ensuremath{\varphi}}}^{4}$ theory in the functional Schr\odinger picture. Our method is the direct generalization of the variational method proposed by Eboli, Jackiw, and Pi for quantum-mechanical systems, and gives the same result as that of Amelino-Camelia and Pi who used the self-consistent composite operator method.

Finite temperature phase transitions in quantum field theory

Using the formalism developed previously the authors discuss finite temperature quantum field theory in the high temperature regime T>>mT where mT represents a generic finite temperature mass in the theory. In particular they consider lambda phi 4 theory in four dimensions showing perturbatively that it has a nontrivial fixed point at finite temperature, the relevant anomalous dimensions near the second-order phase transition being three-dimensional ones. They emphasize the importance of having renormalization schemes and a renormalization group (RG) equation that can explicitly take into account the fact that the degrees of freedom of a theory may be qualitatively different at different scales.

Equation of state for a gas of anyons in a strong magnetic field

Using the hermitian anyonic vertex within finite-temperature quantum field theory, we calculate the grand partition function of a gas of anyons (α-statistics) in a magnetic field near Bose and Fermi statistics. At the first order of α, the closed form of the equation of state for a gas of anyons in the lowest Landau level is obtained. However, at the second order, the closed form for the equation of state seems out of reach. Instead of this, the virial coefficients ( a 2, a 3) are computed at the lowest Landau level.

Relation between real-time and imaginary-time formalisms of finite-temperature quantum field theory.

Perturbative structures of finite-temperature quantum field theory are studied at a fundamental level. It is shown that the real-time formalism based on the Keldysh expansion and the imaginary-time formalism are related by a unitary transformation, and therefore are physically equivalent provided both of them are expressed in retarded form. On the other hand it is impossible for the thermo field dynamics to be reformulated in terms of retarded functions in conformity with the imaginary-time formalism due to the lack of unitary equivalence with the Keldysh and the imaginary-time formalisms which arises from its choice of path in the complex-time plane.

What can we learn from the finite temperature renormalization group?

The renormalization group for finite temperature quantum field theories is studied, in particular for λϕ4. It is shown that the “high” temperature limit can only be discussed perturbatively ifT dependent renormalization schemes are implemented. Zero temperature renormalization schemes or renormalization at some fixed reference temperatureTo are both inadequate as they imply perturbative expansions about fixed points of the renormalization group which are associated with a zero temperature system and a system at temperatureTo respectively.T dependent schemes give rise to an expansion about the true fixed point of the system, the resulting renormalization group allows the entire crossover between high and low temperature behaviour to be investigated.

Temperature and density effects on the one-pion exchange potential

After considering the vacuum polarization and the radiative correction of the nucleon-nucleon-pion (NN\ensuremath{\pi}) system, the one-pion exchange potential with pseudovector coupling or pseudoscalar coupling at finite temperature and finite density is investigated. By using finite-temperature and density quantum field theory, we find that both the pseudovector and pseudoscalar effective coupling of NN\ensuremath{\pi} decrease as temperature and/or density increase, and drop remarkably at high temperature regions and/or high density regions. At a critical temperature ${\mathit{T}}_{\mathit{c}}$ or a critical density ${\mathrm{\ensuremath{\rho}}}_{\mathit{c}}$, the effective NN\ensuremath{\pi} coupling diminishes to zero and the one-pion exchange potential vanishes.

Finite temperature quantum field theory and gauge field

We study the invariance of thermo field dynamics (TFD) for equilibrium systems under local gauge transformations. We show that when restricted to a conveniently constrained subspace of thermal states, TFD has the structure of a gauge theory, the gauge vector field playing the role of the reservoir response to the system dynamics.

Dynamic nonlinear σ model of localization theory

The noninteracting disordered electron system is studied in the framework of a real-time, finite-temperature quantum field theory, the so-called time-path formalism. This formalism enables us to perform an initial-stage disorder averaging without the use of replicas or superfields, leading to an effective action from which disorder averaged quantities can be calculated directly. A “dynamic” nonlinear σ model for a matrix field is derived as an effective theory for the diffusion modes. The matrix field depends on two energy arguments, the external frequency and the characteristic energy scale of interest. These energy arguments play a role similar to the replica or superfield indices. The averaging methods are compared on a perturbative level both in the impurity- and the diffusion-diagram techniques. The loop-contributions, which arise as a consequence of the initial-stage disorder averaging, vanish due to the matrix structure of the diffusion mode. The renormalization of the dynamic nonlinear σ model is shown to lead to the same result as the replica and superfield models.

Stochastic field theory at finite temperature and equilibrium states in quantum statistical mechanics

Stochastic field theory at finite temperature, when it is formulated from stochastic mechanics, which incorporates Brownian motion in both the external, as well as the internal, space of a particle, and the external and internal fields, and which are written as thermal doublets, gives rise to finite temperature quantum field theory in Minkowski space. The Haag–Hugenholtz–Winnik, (HHW) formalism of modular conjugation and the Tomita–Takesaki theory of modular Hilbert algebra then follow from this finite temperature quantum field theoretical formalism. It is shown that there is an inherent discrete Z2 symmetry among the fields of the doublet, and the equilibrium condition is ensured by this symmetry. When this symmetry is spontaneously broken, thermodynamical equilibrium is destroyed.

A dynamic theory of transverse freezing in the Sherrington-Kirkpatrick Ising model

The effect of a transverse field Gamma on spin-glass freezing in the Sherrington-Kirkpatrick version of the quantum Ising model is studied by using the thermo-field-dynamic (TFD) method (the real-time finite-temperature quantum-field theory) due to Takahashi and Umezawa as a substitute for the 'n-replica trick'. An exact effective Lagrangian for the average dynamic causal and response functions is derived by using the functional-integral approach. Furthermore, the properties of the Lagrangian are studied in the mean-field limit by considering the infinite-range random exchange. In this limit the self-consistent equations for the matrix components of the TFD causal Green function are derived with the effective thermal Hamiltonian containing the dynamic spin self-interaction. The static properties of this equation are studied above and below the freezing temperature Tc by extracting the time-delocalised parts of dynamic autocorrelations. The self-consistent equations for the spin-glass order parameter and local susceptibility are obtained. The classical ( Gamma to 0) and quantum (T to 0) limits are discussed. The crucial role of the choice of the thermal-state condition for the spin-glass problem and its striking similarity to the non-equilibrium formulation of the TFD are pointed out.

Nonequilibrium quantum field theories

Abstract Combining the Feynman-Vernon influence functional formalism with the real-time formulation of finite-temperature quantum field theories we present a general approach to relativistic quantum field theories out of thermal equilibrium. We clarify the physical meaning of the additional fields encountered in the real-time formulation of quantum statistics and outline diagrammatic rules for perturbative nonequilibrium computations. We derive a generalization of Boltzmann's equation which gives a complete characterization of relativistic nonequilibrium phenomena.

Transverse freezing in the quantum Ising spin glass: a thermofield dynamic approach

The effect of a transverse field on the spin-glass freezing transition in the Sherrington-Kirkpatrick version of the quantum Ising model is studied using the thermofield dynamics (the real-time, finite-temperature quantum field theory) due to Takahashi and Umezawa (1975) as a substitute for the 'n-replica trick'. The field-dependent transition line to the spin-glass phase is found and the averaged local static metastable susceptibility in the transverse direction is evaluated in the simple mean-field approximation for the effective dynamic Lagrangian.

Real time functional effective action for the quantum dynamics of a transverse Ising model at finite temperature

The method of thermo-field dynamics (TFD, the real time, finite-temperature quantum field theory) for quantum spin algebra has been employed to construct the coarse-grained functional action for the dynamics of the spin-1/2 Ising model in a transverse magnetic field. The applicability of the present approach to the unified treatment of the quantum and classical critical dynamics is pointed out.

Aristotle was right: heavier objects fall faster

According to the weak form of the equivalence principle all objects fall at the same rate in a gravitational field. However, recent calculations in finite-temperature quantum field theory have revealed that at T>0 heavier and/or colder objects actually fall faster than their lighter and/or warmer counterparts. This unexpected result is demonstrated using elementary quantum mechanical arguments.

Finite-temperature quantum field theory in curved spacetime: Quasilocal effective Lagrangians.

We use momentum-space techniques and a quasilocal expansion to derive the imaginary-time thermal Green's functions and the one-loop finite-temperature effective Lagrangians for \ensuremath{\lambda}${\ensuremath{\varphi}}^{4}$ fields in curved spacetimes. These approximations are useful for treating quasiequilibrium conditions associated with gradual changes in the background fields and the background spacetimes. For problems in spacetimes with small curvature, we use a Riemann normal coordinate for the background metric, a derivative expansion for the background field, and a small-proper-time Schwinger-DeWitt expansion to derive the finite-temperature effective Lagrangians. For problems in homogeneous cosmology we consider conformally related fields and the Robertson-Walker universe as background to carry out finite-temperature perturbation calculations. We study a massless conformal \ensuremath{\lambda}${\ensuremath{\varphi}}^{4}$ theory in a Bianchi type-I universe and derive the finite-temperature effective Lagrangian in orders of small anisotropy. The quasilocal method presented here is related to the adiabatic method in finite-temperature quantum field theory presented earlier in similar settings. These results are useful for the study of quantum thermal processes in the early Universe.

Convexity and tadpoles

We show that it is possible to produce a convex effective potential using the tadpole method of calculation, both at zero temperature and in real time finite-temperature quantum field theory. We point out, however, that this does not evade the failure of the loop expansion in a theory with a non-convex classical potential at a temperature where the minima of the effective potential have moved in to the classical points of inflection.

On the quantum field theory of the inhomogeneous electron gas

The equilibrium properties of an inhomogeneous gas of interacting fermions are derived using methods of finite temperature quantum field theory. A Landau-type quasiparticle spectrum yielding the exact ground state energy or, at finite temperatures, the exact thermodynamic potential is constructed from the g-Hartree equations. The heat kernel expansion of Schrödinger operators is then used to express the Hohenberg-Kohn density functional as a series in the quasiparticle density which is asymptotic in the Thomas-Fermi limit. This series is systematically derived from the microscopic action and incorporates boundary effects in an unambiguous manner. The methods developed apply to a large class of field-theoretical models encompassing theories with Yukawa interactions.

Quantum field theory methods and inflationary universe models

This paper reviews the theory of inflationary universe models, giving particular emphasis to the question of origin and growth of energy-density fluctuations in these new cosmologies. The first four sections constitute a pedagogical introduction to some of the important quantum field theory methods used in inflationary universe scenarios: calculation of the effective potential, finite-temperature quantum field theory, analysis of the decay of a metastable quantum state, and free field theory in curved space-time.

Thermo field dynamics of a quantum algebra

Thermo field dynamics (a real-time finite-temperature quantum field theory) is used to construct a reduction formula for the causal multipoint Green function. The method is applicable to the case in which the field operators form some algebra. The application to current problems in physics is suggested.

Thermodynamic calculations in relativistic finite-temperature quantum field theories

A Minkowski space formalism of finite-temperature quantum field theory is used to compute static thermodynamic quantities in the one- and two-loop approximation in an elegant and straightforward way using a generalization of Weinberg's tadpole method of calculating effective potentials. Systematic diagrammatic techniques for low- and high-temperature expansions are developed. Renormalizability by zero-temperature symmetric counterterms is proven for all orders in the loop expansion and demonstrated explicitly to two loops. Many useful computational techniques applicable to general finite temperature calculations are explained.