Related papers: Zeta-regularized vacuum expectation values from qu…
The quantization of the Hamiltonian for a scalar field is performed in the framework of Quantum Reduced Loop Gravity. We outline how the regularization can be performed by using the analogous tools adopted in full Loop Quantum Gravity and…
We establish a novel representation of arbitrary Euler-Zagier sums in terms of weighted vacuum graphs. This representation uses a toy quantum field theory with infinitely many propagators and interaction vertices. The propagators involve…
In this paper we extend the Zeta function regularization technique, which gives a meaningful solution to divergent power series, in order to assign finite values to divergent integral of certain transcendental functions $f(x)$. The…
The machinery of computing vacuum expectation values of a time-ordered sequence of position operators of the simple harmonic oscillator is already well established. It rests on a Wick theorem, which enables one to decompose such a quantity…
The $\beta$ function for a scalar field theory describes the dependence of the coupling constant on the renormalization mass scale. This dependence is affected by the choice of regularization scheme. I explicitly relate the…
A model for quantum Zeno effect based upon an effective Schr\"odinger equation originated by the path-integral approach is developed and applied to a two-level system simultaneously stimulated by a resonant perturbation. It is shown that…
Quantum Electrodynamics (QED) renormalizaion is a paradox. It uses the Euler-Mascheroni constant, which is defined by a conditionally convergent series. But Riemann's series theorem proves that any conditionally convergent series can be…
In this paper it is shown how the generating functional for Green's functions in relativistic quantum field theory and in thermal field theory can be evaluated in terms of a standard quantum mechanical path integral. With this calculational…
We calculate the scattering amplitude in the two dimensional $CP(1)$ model in a regularization scheme independent way. When using cutoff regularization, a new Feynman rule from the path integral measure is required if one is to preserve the…
Feynman's model of a quantum computer provides an example of a continuous-time quantum walk. Its clocking mechanism is an excitation of a basically linear chain of spins with occasional controlled jumps which allow for motion on a planar…
We calculate normalization factors and reflection amplitudes in the W-invariant conformal quantum field theories. Using these CFT data we derive vacuum expectation values of exponential fields in affine Toda theories and related perturbed…
Our goal in this paper is to present a generalization of the spectral zeta regularization for general Feynman amplitudes. Our method uses complex powers of elliptic operators but involves several complex parameters in the spirit of the…
We describe a quantum algorithm that solves combinatorial optimization problems by quantum simulation of a classical simulated annealing process. Our algorithm exploits quantum walks and the quantum Zeno effect induced by evolution…
Efforts to give an improved mathematical meaning to Feynman's path integral formulation of quantum mechanics started soon after its introduction and continue to this day. In the present paper, one common thread of development is followed…
The proper definition and evaluation of the configuration space path integral for the motion of a particle in curved space is a notoriously tricky problem. We discuss a consistent definition which makes use of an expansion in Fourier sine…
A divergence-free approach to relativistic quantum electrodynamics based on regularisation of equations of quantum mechanics is discussed. This approach is shown to be exactly equivalent to the conventional Feynman-Dyson renormalisation…
We develop precise formulation for the effects of vacuum polarization near a pointlike source with a zero-range ($\delta$-like) potential in three spatial dimensions. There are different ways of introducing $\delta$-interaction in the…
We obtain, through zeta function methods, the one-loop effective action for massive Dirac fields in the presence of a uniform, but otherwise general, electromagnetic background. After discussing renormalization, we compare our zeta function…
We consider the quantum computational process as viewed by an insider observer: this is equivalent to an isomorphism between the quantum computer and a quantum space, namely the fuzzy sphere. The result is the formulation of a reversible…
The new emerging quantum physics - quantum computing conceptual bridge, mandates a ``grand unification'' of space-time-matter and quantum information (all quantized), with deep implications for science in general. The major physics…