Related papers: The Stress-Energy Operator
We consider the Hawking-Ellis (Segre-Plebanski) classification of stress-energy tensors, both in the test-field limit, and in the presence of back-reaction governed by the usual Einstein equations. For test fields it is not too difficult to…
We provide geometric quantization of a completely integrable Hamiltonian system in the action-angle variables around an invariant torus with respect to the angle polarization. The carrier space of this quantization is the pre-Hilbert space…
In this paper we introduce an alternative approach to studying the evolution of a quantum harmonic oscillator subject to an arbitrary time dependent force. With the purpose of finding the evolution operator, certain unitary transformations…
We define C*-algebras on a Fock space such that the Hamiltonians of quantum field models with positive mass are affiliated to them. We describe the quotient of such algebras with respect to the ideal of compact operators and deduce…
Let $A$ and $B$ be local operators in Hamiltonian quantum systems with $N $ degrees of freedom and finite-dimensional Hilbert space. We prove that the commutator norm $\lVert [A(t),B]\rVert$ is upper bounded by a topological combinatorial…
For a scalar evolution equation $u_t=K(t,x,u,u_x,\ldots, u_n), n\geq 2$ the cohomology spaces $H^{1,s}({\mathcal R}^\infty)$ vanishes for $s\geq 3$ while the space $H^{1,2}({\mathcal R}^\infty)$ is isomorphic to the space of variational…
We study the spectrum of a random Schroedinger operator for an electron submitted to a magnetic field in a finite but macroscopic two dimensional system of linear dimensions equal to L. The y direction is periodic and in the x direction the…
We propose how to compute the complexity of operators generated by Hamiltonians in quantum field theory (QFT) and quantum mechanics (QM). The Hamiltonians in QFT/QM and quantum circuit have a few essential differences, for which we…
We introduce a self-adjoint time operator $T_w = i\hbar\bigl(\partial_E + \tfrac12\,\partial_E\ln w(E)\bigr)$ on the weighted energy space $L^2(\mathbb R,\,w(E)\,dE)$. Under mild conditions on the weight $w$ (positivity, local absolute…
We study scalar (not necessarily conformal) quantum fields on self-similar spacetimes. It is shown that in states respecting the self-similarity the expectation value of the stress tensor gives rise to a Lyapunov exponent $\omega_q = 2$,…
Hamiltonian and Schrodinger evolution equations on finite-dimensional projective space are analyzed in detail. Hartree-Fock (HF) manifold is introduced as a submanifold of many electron projective space of states. Evolution equations, exact…
We study the behavior of a massless, quantized, scalar field on a two-dimensional cylinder spacetime as it responds to the time-dependent evolution of a Mamev-Trunov potential of the form $V(x,t) = 2 \xi \delta(x) \theta(-t)$. We begin by…
We have derived several relations, which allow the evaluation of the system free energy changes in the leading order in $\hbar^{2}$ along classically generated trajectories. The results are formulated in terms of purely classical…
We calculate the operator complexity for the displacement, squeeze and rotation operators of a quantum harmonic oscillator. The complexity of the time-dependent displacement operator is constant, equal to the magnitude of the coherent state…
We obtain the complexity geometry associated with the Hamiltonian of a quantum mechanical system, specifically in cases where the Hamiltonian is explicitly time-dependent. Using Nielsen's geometric formulation of circuit complexity, we…
We consider a self-interacting, massive, real scalar field on a four-dimensional globally hyperbolic spacetime and the associated stress-energy tensor. Using techniques proper of the algebraic approach to perturbative quantum field theory,…
The components of the renormalized quantum stress tensor for a massive vector field in the spacetime of a pointlike global monopole are determined analytically in the Schwinger-DeWitt approximation. The general results are employed to…
Representations of the quantum q-oscillator algebra are studied with particular attention to local Hamiltonian representations of the Schroedinger type. In contrast to the standard harmonic oscillators such systems exhibit a continuous…
The necessity of rejecting the numerical model of geometrical extension is postulated on the basis of the idea of identity of space-time and physical vacuum. An attempt is made to define space-time not via the concept of manifold, but via…
According to a recent suggestion [1], the energy--momentum tensor for gravitating fields can be computed through a suitable rearrangement of the matter field equations, without relying on the variational definition. We show that the…