Related papers: Complex Classical Fields: A Framework for Reflecti…
We give a mathematical construction of Euclidean quantum field theory on certain curved backgrounds. We focus on generalizing Osterwalder-Schrader quantization, as these methods have proved useful to establish estimates for interacting…
We study the quantization of certain classical field theories using reflection positivity. We give elementary conditions that ensure the resulting vacuum state is cyclic for products of quantum field operators, localized in a bounded…
Reflection positivity constitutes an integral prerequisite in the Osterwalder-Schrader reconstruction theorem which relates quantum field theories defined on Euclidean space to their Lorentzian signature counterparts. In this work we…
The requirement of reflection positivity(RP) for Euclidean field theories is considered. This is done for the cases of a scalar field, a higher derivative scalar field theory and the scalar field theory defined on a non-integer dimensional…
A basic problem in quantizing a field in curved space is the decomposition of the classical modes in positive and negative frequency. The decomposition is equivalent to a choice of a complex structure in the space of classical solutions. In…
This paper discusses the general structure of reflection positive Euclidean covariant distributions that can be used to construct Euclidean representations of relativistic quantum mechanical models of systems of a finite number of degrees…
The concept of reflection positivity has its origins in the work of Osterwalder--Schrader on constructive quantum field theory. It is a fundamental tool to construct a relativistic quantum field theory as a unitary representation of the…
We present a derivation of the effect of the classical field configuration to the diffusion equations. Using the formalism of the thermo field dynamics we propose a systematic and consistent way to treat the classical background and to…
The notions of reflection, symmetry, and positivity from quantum field theory are shown to induce a duality operation for a general class of unitary representations of Lie groups. The semisimple Lie groups which have this $c$-duality are…
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 study some examples of complex, classical, scalar fields within the new framework that we introduced in a previous work. In these particular examples, we replace the usual functional integral by a complex functional arising from partial…
We do a critical review of the Faraday-Maxwell concept of classical field and of its quantization process. With the hindsight knowledge of the essentially quantum character of the interactions, we use a naive classical model of field, based…
We adopt the general formalism, which was developed in Paper I (arXiv:0708.1233) to analyze the evolution of a quantized time-dependent oscillator, to address several questions in the context of quantum field theory in time dependent…
For classical field theories with probabilistic initial conditions the classical field observables are an idealization. Their arbitrarily precise values poorly reflect the characteristic uncertainty in the presence of substantial…
A Euclidean formulation of relativistic quantum mechanics for systems of a finite number of degrees of freedom is discussed. Relativistic treatments of quantum theory are needed to study hadronic systems at sub-hadronic distance scales.…
Globally-constrained classical fields provide a unexplored framework for modeling quantum phenomena, including apparent particle-like behavior. By allowing controllable constraints on unknown past fields, these models are retrocausal but…
We study the evolution of the coupled scalar and fermion fields within the classical field theory. We examine the case of N coupled fields in 1+3 dimensional space. The general expressions for the fields distributions are obtained. The…
We investigate stochastic quantization as a method to go from a classical PDE (with stochastic time $\lambda$) to a corresponding quantum theory in the limit $\lambda\to\infty$. We test the method for a linear PDE satisfied by the free…
A quantum field theory is described which is a supersymmetric classical model. -- Supersymmetry generators of the system are used to split its Liouville operator into two contributions, with positive and negative spectrum, respectively. The…
Within the context of piecewise linear manifolds we establish reflection positivity with a Hilbert action given in terms of the Regge curvature and a cosmological term. Using this positivity a Hilbert space for a quantum theory is…