Related papers: Is the Euclidean path integral always equal to the…
In perturbative calculations of quantum-statistical zero-temperature path integrals in curvilinear coordinates one encounters Feynman diagrams involving multiple temporal integrals over products of distributions, which are mathematically…
We derive the partition function of the one-body and two-body systems of classical noncommutative harmonic oscillator in two dimensions. Then, we employ the path integral approach to the quantum noncommutative harmonic oscillator and derive…
The relation between the covariant Euclidean free-energy $F^E$ and the canonical statistical-mechanical free energy $F^C$ in the presence of the Killing horizons is studied. $F^E$ is determined by the covariant Euclidean effective action.…
We give here a covariant definition of the path integral formalism for the Lagrangian, which leaves a freedom to choose anyone of many possible quantum systems that correspond to the same classical limit without adding new potential terms…
In this contribution we describe some interesting interplay between quantum theory, general relativity and thermodynamics. In order to highlight the connection between these theories, we describe two approaches that allow to calculate…
Recent investigations revealed that the near horizon Hamiltonian of a massless, chargeless outgoing particle, for its particular motion in static as well as stationary black holes, is effectively $\sim xp$ kind. This is unstable by nature…
Quantum mechanics requires a hermitian inner product <~,~> -- linear in one variable, antilinear in the other -- while the inner product (~,~) that comes most naturally from Euclidean path integrals is linear in each variable. Here we…
The decay rate for a particle in a metastable cubic potential is investigated in the quantum regime by the Euclidean path integral method in semiclassical approximation. The imaginary time formalism allows one to monitor the system as a…
We establish the link between the thermodynamics and the quantum theory of black hole horizons through the construction of the thermodynamic partition function, partly based on some physically plausible arguments, by beginning from the…
Path integrals are a central tool when it comes to describing quantum or thermal fluctuations of particles or fields. Their success dates back to Feynman who showed how to use them within the framework of quantum mechanics. Since then, path…
It is well-known that the results by Bekenstein, Gibbons and Hawking on the thermodynamics of black holes can be reproduced quite simply in the Euclidean path integral approach to Quantum Gravity. The corresponding partition function is…
Linde's proposal of a Euclidean path integral with the ``wrong'' sign of Euclidean action is often identified with the tunneling proposal for the wave function of the universe. However, the two proposals are in fact quite different. I…
On the basis of the canonical quantization procedure, in which we need the indefinite metric Hilbert space, we formulate field diagonal representation for the scalar Lee-Wick model. Euclidean path integral for the model is then constructed…
Building on initial work on the Thermodynamic Split Conjecture (TSC), which posits that black hole and cosmological horizon thermodynamics are generically inequivalent, we examine the consequences of that split for the Gibbons Hawking…
Starting from the canonical formalism of relativistic (timeless) quantum mechanics, the formulation of timeless path integral is rigorously derived. The transition amplitude is reformulated as the sum, or functional integral, over all…
We consider a microscopic model of spacetime, where spacetime is assumed to be a specific graph with Planck size quantum black holes on its vertices. As a thermodynamical system under consideration we take a certain uniformly accelerating,…
We show that the requirement of manifest coordinate invariance of perturbatively defined quantum-mechanical path integrals in curved space leads to an extension of the theory of distributions by specifying unique rules for integrating…
The notions of temperature, entropy and `evaporation', usually associated with spacetimes with horizons, are analyzed using general approach and the following results, applicable to different spacetimes, are obtained at one go. (i) The…
In this paper we describe two approaches that allow to calculate some thermal features as perceived by different observers in curved spacetimes: the tunnelling method and the Unruh-DeWitt detector. The tunnelling phenomenon is a…
An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to…