Related papers: Classical and Quantum Fields on Lorentzian Manifol…
Hybrid quantum-classical neural networks represent a promising frontier in the search for improved machine learning models. This thesis explores the integration of quantum layers within classical convolutional neural network architectures,…
A mathematically rigorous Hamiltonian formulation for classical and quantum field theories is given. New results include clarifications of the structure of linear fields, and a plausible formulation for nonlinear fields. Many mathematical…
The practice of setting quantum fields as sources for classical general relativity is examined. Several conceptual problems are identified which invalidate apparently innocuous equations. Alternative ways to links classical general…
The dynamics of a Brownian particle in a constant magnetic field and time-dependent electric field is studied in the limit of white noise, using a Langevin approach for the classical problem and the path-integral Feynman-Vernon and…
The existence of a classical limit describing interacting particles in a second-quantized theory of identical particles with bosonic symmetry is proved. This limit exists in addition to a previously established classical limit with a…
In this paper we will analyse some interesting structures that occur in scalar quantum field theory. We will quantize this theory using path integrals. We will analyse the Bogomolny Bound for scalar quantum field theory in two dimensions.…
We propose a new quantum approach for describing a system of $n$ interacting particles with variable mass connected by an unknown field with variable form ($n$-VMVF systems). Instead of assuming any particular nature for variation of the…
It is shown that every algebraic quantum field theory has an underlying functorial field theory which is defined on a suitable globally hyperbolic Lorentzian bordism pseudo-category. This means that globally hyperbolic Lorentzian bordisms…
We discuss Born-Infeld type fields (tachyon fields) in classical and quantum cosmology. We first partly review and partly extend the discussion of the classical solutions and focus in particular on the occurrence of singularities. For…
The dynamics of quantum field theories on bounded domains requires the introduction of boundary conditions on the quantum fields. We address the problem from a very general perspective by using charge conservation as a fundamental principle…
We introduce the concept of pseudo-reality for complex numbers. We show that this concept, applied to quantum fields, provides a unifying framework for two distinct approaches to pseudo-Hermitian quantum field theories. The first approach…
We consider the problem of quantum-classical correspondence in integrable field theories. We propose a method to construct a field theoretical coherent state, in which the expectation value of the quantum field operator exactly coincides…
We give a microscopic derivation of perturbative quantum field theory, taking causal fermion systems and the framework of the fermionic projector as the starting point. The resulting quantum field theory agrees with standard quantum field…
Local quantum fields in 1+1 dimensions can have bounded field operators. The class of such fields which in addition obey Huygens' principle (time-like commutativity) and conformal covariance, is completely determined.
In this paper, we present a quantum-field-theoretical description of the interaction between stationary and localized external sources linearly coupled to bosonic fields (specifically, we study models with a scalar and the Maxwell field).…
The long-standing challenge to describing charged particle dynamics in strong classical electromagnetic fields is how to incorporate classical radiation, classical radiation reaction and quantized photon emission into a consistent unified…
We propose a mathematical model of quantum spacetime as an infinite-dimensional manifold locally homeomorphic to an appropriate Schwartz space. This extends and unifies both the standard function space construction of quantum mechanics and…
In the 1-dimensional matrix model one identifies the tachyon field in the asymptotic region with a nonlocal transform of the density of fermions. But there is a problem in relating the classical tachyon field with the surface profile of the…
We elaborate further the functional Schr\"{o}dinger-picture approach to the quantum field in curved spacetimes using the generalized invariant method and construct explicitly the Fock space, which we relate with the thermal field theory. We…
Covariant generalizations of well-known wave equations predict the existence of inertial-gravitational effects for a variety of quantum systems that range from Bose-Einstein condensates to particles in accelerators. Additional effects arise…