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The construction of the known interacting quantum field theory models is mostly based on euclidean techniques. The expectation values of interesting quantities are usually given in terms of euclidean correlation functions from which one…
Explicit solution of a Green function in a non-renormalizable toy model demonstrates that Green functions of the interacting theory fall off much faster than at the tree level at large momenta. This suggests a method of calculations in…
Guided by idealized but soluble nonrenormalizable models, a nontraditional proposal for the quantization of covariant scalar field theories is advanced, which achieves a term-by-term, divergence-free perturbation analysis of interacting…
We present a model of interacting quantum fields, formulated in a non-perturbative manner. One of the fields is treated semi-classically, the other is the photon field. The model has an interpretation of an electromagnetic field in a…
The capabilities of the functional-analytic and of the functional-integral approach for the construction of the Hamiltonian as a self-adjoint operator on Hilbert space are compared in the context of non-relativistic quantum mechanics.…
In quantum field theory, it is generally assumed that there is a lower bound to the energy, which is normally assumed to the the vacuum state. While this may be a reasonable assumption for a free field it is not necessarily the case for…
The quantum theory of fields is largely based on studying perturbations around non-interacting, or free, field theories, which correspond to a collection of quantum-mechanical harmonic oscillators. The quantum theory of an ordinary fluid is…
We study a general field theory of a scalar field coupled to gravity through a quadratic Gauss-Bonnet term $\xi(\phi) R^2_{GB}$. The coupling function has the form $\xi(\phi)=\phi^n$, where $n$ is a positive integer. In the absence of the…
We construct a quantum theory of free scalar field in 1+1 dimensions based on a `Generalized Uncertainty Principle'. Both canonical and path integral formalism are employed. Higher dimensional extension is easily performed in the path…
This work has a methodological nature and is a set of lecture notes for undergraduate students. It is devoted to the study of the basic tools of quantum field theory on the example of the simplest cubic "toy" model. We introduce such…
The degrees of freedom of any interacting quantum field theory are entangled in momentum space. Thus, in the vacuum state, the infrared degrees of freedom are described by a density matrix with an entanglement entropy. We derive a relation…
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 functional integral has many triumphs in elucidating quantum theory. But incorporating charge fractionalization into that formalism remains a challenge.
We consider the problem of evolving a quantum field between any two (in general, curved) Cauchy surfaces. Classically, this dynamical evolution is represented by a canonical transformation on the phase space for the field theory. We show…
We study a class of universal Feynman integrals which appear in four-dimensional holomorphic theories. We recast the integrals as the Fourier transform of a certain polytope in the space of loop momenta (aka the ``Operatope''). We derive a…
Feynman path integrals are now a standard tool in quantum physics and their use in differential geometry leads to new mathematical insights. A logical treatment of quantum phenomena seems to require a sustained mathematical analysis of path…
In the operational approach to general probabilistic theories one distinguishes two spaces, the state space of the "elementary systems" and the physical space in which "laboratory devices" are embedded. Each of those spaces has its own…
We construct in a rigorous mathematical way interacting quantum field theories on a p-adic spacetime. The main result is the construction of a measure on a function space which allows a rigorous definition of the partition function. The…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
We review the status of (scalar) quantum field theory on curved spacetimes using a novel formulation in terms of non linear functionals over the smooth configuration fields. In particular, this entails also a new foundation of locally…