相关论文: Quantum propagators in a random metric

In the limit of large quantum excitations, the classical and quantum probability distributions for a Schr\"odinger equation can be compared by using the corresponding WKBJ solutions whose rapid oscillations are averaged. This result is…

Despite the fact that it has been known since the time of Heisenberg that quantum operators obey a quantum version of Newton's laws, students are often told that derivations of quantum mechanics must necessarily follow from the Hamiltonian…

This work deals with Schr\"odinger equations with quadratic and sub-quadratic Hamiltonians perturbed by a potential. In particular we shall focus on bounded, but not necessarily smooth perturbations. We shall give a representation of such…

We comment on the recent attempt by M. Franz et al [1] to further justify their earlier calculation of the gauge-invariant electron propagator in the context of the QED_3 theory of the pseudogap phase in cuprates [2]. First, we use the…

Contrary to what is often stated, a fundamental spacetime discreteness need not contradict Lorentz invariance. A causal set's discreteness is in fact locally Lorentz invariant, and we recall the reasons why. For illustration, we introduce a…

A variational method is discussed, based on the principle of minimal variance. The method seems to be suited for gauge interacting fermions, and the simple case of quantum electrodynamics is discussed in detail. The issue of renormalization…

We make a proposal for gauge-invariant observables in perturbative quantum gravity in cosmological spacetimes, building on the recent work of Brunetti et al. [JHEP 08 (2016) 032]. These observables are relational, and are obtained by…

We consider the most general action for gravity which is quadratic in curvature. In this case first order and second order formalisms are not equivalent. This framework is a good candidate for a unitary and renormalizable theory of the…

The linearized Einstein field equations provide a low-energy wave equation for the propagation of gravitational fields which may originate from a high energy source. Motivated by loop quantum gravity, we propose the polymer quantization…

We solve the Dyson--Schwinger equation for the quark propagator in a model with singular infrared behavior for the gluon propagator. We require that the solutions, easily found in configuration space, be tempered distributions and thus have…

We show that the special relativistic dynamics when combined with quantum mechanics and the concept of superstatistics can be interpreted as arising from two interlocked non-relativistic stochastic processes that operate at different energy…

A new approximation scheme for non-perturbative calculations in a quantum field theory is proposed. The scheme is based on investigation of solutions of the Schwinger equation with its singular character taken into account. As a necessary…

Quantum mechanics is sensitive to the geometry of the underlying space. Here, we present a framework for quantum scattering of a non-relativistic particle confined to a two-dimensional space. When the motion manifold hosts localized…

Fully covariant wave equations predict the existence of a class of inertial-gravitational effects that can be tested experimentally. In these equations inertia and gravity appear as external classical fields, but, by conforming to general…

We show how to deal with the generalized q-Schr\"odinger and q-Klein-Gordon fields in a variety of scenarios. These q-fields are meaningful at very high energies (TeVs) for for $q=1.15$, high ones (GeVs) for $q=1.001$, and low energies…

We present a first-quantized formulation of the quadratic non-commutative field theory in the background of abelian (gauge) field. Even in this simple case the Hamiltonian of a propagating particle depends non-trivially on the momentum…

We improve on Cutkosky's cutting rules which is used to calculate the contribution of the singularities of Feynman propagators to Feynman amplitude. The correctness of the improved cutting rules is verified by the calculations of the…

In this note we study the properties of a sequence of approximate propagators for the Schr\"odinger equation, in the spirit of Feynman's path integrals. Precisely, we consider Hamiltonian operators arising as the Weyl quantization of a…

Quantum-mechanical wave equation for a particle with spin 1 is investigated in presence of external magnetic field in spaces with non-Euclidean geometry with constant positive curvature. Separation of the variable is performed; differential…

The fractional operators together with exponential quantum in coordinate and momentum space corresponding to the power of observables are introduced. Based on an exponential relation between energy and momentum, the fractional Schr\"odinger…