Related papers: Regularization by Test Function
A convenient way to calculate $N$-particle quantum partition functions is by confining the particles in a weak harmonic potential instead of using a finite box or periodic boundary conditions. There is, however, a slightly different…
Quantum physics can only make statistical predictions about possible measurement outcomes, and these predictions originate from an operator algebra that is fundamentally different from the conventional definition of probability as a…
We stress the notion of statistical experiment, which is mandatory for quantum mechanics, and recall Ludwig's foundation of quantum mechanics, which provides the most general framework to deal with statistical experiments giving evidence…
Simulating key static and dynamic properties of matter -- from creation in the Big Bang to evolution into sub-atomic and astrophysical environments -- arising from the underlying fundamental quantum fields of the Standard Model and their…
Physics in the vicinity of an ultraviolet stable fixed point of a quantum field theory is parametrized by a renormalization group invariant macroscopic length scale, the correlation length $\xi,$ with the quantum effective action a function…
Physical processes in the quantum regime possess non-classical properties of quantum mechanics. However, methods for quantitatively identifying such processes are still lacking. Accordingly, in this study, we develop a framework for…
The canonical approach to quantum gravity has been put on a firm mathematical foundation in the recent decades. Even the quantum dynamics can be rigorously defined, however, due to the tremendously non-polynomial character of the…
Today's quantum field theory (QFT) relies heavenly on canonical quantization (CQ), which fails for $\varphi^4_4$ leading only to a "free" result. Affine quantization (AQ), an alternative quantization procedure, leads to a "non-free" result…
We outline, test, and apply a new scheme for nonpertubative analyses of quantized field systems in contact with dynamical gravity. While gravity is treated classically in the present paper, the approach lends itself for a generalization to…
We use tools from non-standard analysis to formulate the building blocks of quantum field theory within the framework of categorical quantum mechanics. Building upon previous work, we construct an object of *Hilb having quantum fields as…
The quantum mechanical equivalent of parametric resonance is studied. A simple model of a periodically kicked harmonic oscillator is introduced which can be solved exactly. Classically stable and unstable regions in parameter space are…
The coupling between internal degrees of freedom of quantum systems and their overall motion in an external gravitational field plays a central role in multiple extensions of Einstein's equivalence principle to quantum physics. While…
Renormalization group ideas and effective operators are used to efficiently determine localized unitaries for preparing the ground states of non-interacting scalar field theories on digital quantum devices. With these methods, classically…
A rigorous microscopic theory for the description of quantum-transport phenomena in systems with open boundaries is proposed. We shall show that the application of the conventional Wigner-function formalism to this problem leads to…
A fundamental problem with attempting to quantize general relativity is its perturbative non-renormalizability. However, this fact does not rule out the possibility that non-perturbative effects can be computed, at least in some…
With the present trend in experimental particle physics of probing yet shorter distances and with the requirement on the theoretical side of renormalizability, conformal invariance becomes an attractive symmetry for particle interactions.…
Quantum field theory currently has a single standard mathematical characterization (the Standard Model), but no single accepted conceptual framework to interpret the mathematics. Many of these conceptualizations rely on intuitive concepts…
A class of unitary operations generated by idealized, semiclassical fields is studied. The operations implemented by sharp potential kicks are revisited and the possibility of performing them by softly varying external fields is examined.…
The standard model of the quantum theory of measurement is based on an interaction Hamiltonian in which the observable-to-be-measured is multiplied with some observable of a probe system. This simple Ansatz has proved extremely fruitful in…
The ``evolving constants'' method of defining the quantum dynamics of time-reparametrization-invariant theories is investigated for a particular implementation of parametrized non-relativistic quantum mechanics (PNRQM). The wide range of…