A note on classical and quantum unimodular gravity

We discuss unimodular gravity at a classical level, and in terms of its extension into the UV through an appropriate path integral representation. Classically, unimodular gravity is locally a gauge fixed version of general relativity (GR), and as such it yields identical dynamics and physical predictions. We clarify this and explain why there is no sense in which it can “bring a new perspective” to the cosmological constant problem. The quantum equivalence between unimodular gravity and GR is more of a subtle question, but we present an argument that suggests one can always maintain the equivalence up to arbitrarily high momenta. As a corollary to this, we argue, whenever inequivalence is seen at the quantum level, that just means we have defined two different quantum theories that happen to share a classical limit. We also present a number of alternative formulations for a covariant unimodular action, some of which have not appeared, to our knowledge, in the literature before.     

Finite thermostats in classical and quantum nonequilibrium

Models for studying systems in stationary states but out of equilibrium have often empirical nature and very often break the fundamental time reversal symmetry. Here, a formal interpretation will be discussed of the widespread idea that, in any event, the particular friction model choice should not matter physically. The proposal is, quite generally, that for the same physical system a time reversible model should be possible. Examples about the Navier–Stokes equations are given.     

Finite field-dependent symmetries in perturbative quantum gravity

In this paper we discuss the absolutely anticommuting nilpotent symmetries for perturbative quantum gravity in general curved spacetime in linear and non-linear gauges. Further, we analyze the finite field-dependent BRST (FFBRST) transformation for perturbative quantum gravity in general curved spacetime. The FFBRST transformation changes the gauge-fixing and ghost parts of the perturbative quantum gravity within functional integration. However, the operation of such symmetry transformation on the generating functional of perturbative quantum gravity does not affect the theory on physical ground. The FFBRST transformation with appropriate choices of finite BRST parameter connects non-linear Curci–Ferrari and Landau gauges of perturbative quantum gravity. The validity of the results is also established at quantum level using Batalin–Vilkovisky (BV) formulation.     

Phenomenological description of quantum gravity inspired modified classical electrodynamics

We discuss a large class of phenomenological models incorporating quantum gravity motivated corrections to electrodynamics. The framework is that of electrodynamics in a birefringent and dispersive medium with non-local constitutive relations, which are considered up to second order in the inverse of the energy characterizing the quantum gravity scale. The energy-momentum tensor, Green functions and frequency dependent refraction indices are obtained, leading to departures from standard physics. The effective character of the theory is also emphasized by introducing a frequency cutoff Ω. The analysis of its effects upon the standard notion of causality is performed, showing that in the radiation regime (Ω R ≫ 1) the expected corrections of the order (ω/Ω) ⁿ get further suppressed by highly oscillating terms proportional to , thus forbiding causality violations to show up in the corresponding observational effects. Dedicated to Octavio Obregón on his sixtieth birthday.     

Finite temperature effects in quantum field theory

We consider quantum electrodynamics at finite temperatures. By making use of the real time formalism we compute, on the one-loop level, the finite-temperature correction to the mass of the electron and to the anomalous magnetic moment a_e^th. The gauge-invariant correction to the electron mass is found to be a ten percent effect at a temperature of the order of 2×10¹⁰ K. Some astrophysical implications of this result are briefly discussed. The leading temperature correction to the anomalous magnetic moment of the electron is, at a temperature of 300 K, found to be one order of magnitude smaller than the τ-lepton contribution to a_e^th.     

Finite temperature formalism for composite quantum particles

This Letter provides the missing part of the newly constructed many-body formalism for composite quantum particles: the introduction of a finite temperature. The finite T formalism we propose deeply relies on the existence of a compact closure relation for the (overcomplete) set of N-composite-particle states. As a first application, we here calculate the energy mean value of the exciton gas outside the condensation regime. We show that carrier exchanges increase its temperature dependence compared to elementary bosons, a signature of the degree-of-freedom increase resulting from the particle composite nature.     

Induced classical gravity

We review the induced-gravity approach according to which the Einstein gravity is a long-wavelength effect induced by underlying fundamental quantum fields due to the dynamical-scale symmetry breaking. It is shown that no ambiguities arise in the definition of the induced Newton and cosmological constants if one works with the path integral for fundamental fields in the low-scale region. The main accent is on a specification of the path integral which enables us to utilize the unitarity condition and thereby avoid ambiguities. Induced Einstein equations appear from the symmetry condition that the path integral of fundamental fields for a slowly varying metric is invariant under the local GL(4, R)-transformations of a tetrad, which contain the local Euclidean Lorentz, O(4)-rotations as a subgroup. The relationship to induced quantum gravity is briefly outlined.     

Finite temperature quantum fields in expanding universes

The thermodynamics of an ideal relativistic quantum gas in expansion is studied. It is found that only for conformally invariant fields in conformally static spacetime can thermal equilibrium be strictly maintained. A finite temperature theory can be defined under the condition of quasi equilibrium when the background expansion is nearly adiabatic. The high temperature expansion of the energy density for massive nonconformal fields in Robertson-Walker universes and for conformal fields in Bianchi Type-I universes are calculated. The importance of these results on phase transition and quantum processes in the early universe is discussed.     

Bohm's quantum potentials and quantum gravity

A generally covariant theory, written in the spirit of Bohm's theory of quantum potentials, which applies to spinless, non interacting, gravitating systems, is formulated. In this theory the quantum state is coupled to the metric tensor g, and the effect of the quantum potential is absorbed in the geometry. At the same time, satisfies a covariant wave equation with respect to the very same g. This provides sufficient constraints to derive 11 coupled equations in the 11 unknowns: and the components of the metric tensor g_µv. The states of stable localized particles are identified, and vacuum-state solutions for both the Euclidean and the Lorentzian case are explicitly presented.     

Summary of session A4: Complex and conformal methods in classical and quantum gravity

This paper summarises oral contributions to the parallel session Complex and conformal methods in classical and quantum gravity which took place during the 20th International Conference on General Relativity and Gravitation held in Warsaw in July 2013.     

Arrow of time, parity violation, and gravity in generalized quantum and classical dynamics

The quantum mechanics with a stationary non-Hermitian Hamiltonian and a complex evolution parameter, as well as its classical limit with nontrivial correlations have been studied. The corresponding dynamics is shown to be irreversible for the isothermal and adiabatic regimes of quantum and classical evolution. The possibility of a universal relationship between irreversibility and dynamical parity violation in the system has been established. The mechanism of gravity generation by the distribution of correlations in a free theory is demonstrated.     

Time and quantum gravity

The role of time in the interpretation of quantum mechanics and quantum gravity are analyzed, and changes to the form of quantum gravity to make it interpretable are suggested.     

Logics and quantum gravity

We consider the logic needed for models of quantum gravity, taking as our starting point a simple pregeometric toy model based on graph theory. First a discussion of quantum logic seen in the light of canonical quantum gravity is given, then a simple toy model is proposed and the logical structure underlying it exposed. It is then shown that this logic is nonclassical and in fact contains quantum logics as special cases. We then go on to show how Yang-Mills theory and quantum mechanics fits in. A single mathematical structure is proposed capable of containing all these subjects in a natural and elegant way. Causality plays an important role. The mere presence of a causal relation almost inevitably yields this kind of logic.     

Low temperature phase diagrams for quantum perturbations of classical spin systems

We consider a quantum spin system with Hamiltonian $$H = H^{(0)} + \lambda V,$$ whereH ⁽⁰⁾ is diagonal in a basis ∣s〉=? _x ∣s _x 〉 which may be labeled by the configurationss={s_x} of a suitable classical spin system on ? ^d , $$H^{(0)} |s\rangle = H^{(0)} (s)|s\rangle .$$ We assume thatH ⁽⁰⁾(s) is a finite range Hamiltonian with finitely many ground states and a suitable Peierls condition for excitation, whileV is a finite range or exponentially decaying quantum perturbation. Mapping thed dimensional quantum system onto aclassical contour system on ad+1 dimensional lattice, we use standard Pirogov-Sinai theory to show that the low temperature phase diagram of the quantum spin system is a small perturbation of the zero temperature phase diagram of the classical HamiltonianH ⁽⁰⁾, provided λ is sufficiently small. Our method can be applied to bosonic systems without substantial change. The extension to fermionic systems will be discussed in a subsequent paper.