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Quantum neural networks (QNNs) use parameterized quantum circuits with data-dependent inputs and generate outputs through the evaluation of expectation values. Calculating these expectation values necessitates repeated circuit evaluations,…
We regularize in a continuous manner the path integral of QED by construction of a non-local version of its action by means of a regularized form of Dirac's $\delta$ functions. Since the action and the measure are both invariant under the…
A possible way toward the quantization of a weak gravitational field inspired by the imaginary-time field theory is discussed. The analogies of the general relativity in the canonical formulation with the thermodynamic geometry and…
The scalar, vector, and tensor components of the (generalized) deuteron electric polarizability are calculated, as well as their logarithmic modifications. Several of these quantities arise in the treatment of the nuclear corrections to the…
We summarize the application of the field--antifield formalism to the quantization of gauge field theories. After the gauge fixing, the main issues are the regularization and anomalies. We illustrate this for chiral $W_3$ gravity. We…
The Wick rotation in quantum field theory is considered in terms of analytical continuation in the signature matrix parameter w = eta_00. Regularization of propagators by a complex metric parameter in most cases preserves (i) the…
When calculating next-to-leading order QCD cross sections, divergences in intermediate steps of the calculation must be regularized. The final result is independent of the regularization scheme used, provided that it is unitary. In this…
It is shown that Euclidean field theory with polynomial interaction, can be regularized using the wavelet representation of the fields. The connections between wavelet based regularization and stochastic quantization are considered.
The requirement of general covariance of quantum field theory (QFT) naturally leads to quantization based on the manifestly covariant De Donder-Weyl formalism. To recover the standard noncovariant formalism without violating covariance,…
Regularisation theory in Banach spaces, and non--norm-squared regularisation even in finite dimensions, generally relies upon Bregman divergences to replace norm convergence. This is comparable to the extension of first-order optimisation…
\emph{Koopman Regularization} is a constrained optimization-based method to learn the governing equations from sparse and corrupted samples of the vector field. \emph{Koopman Regularization} extracts a functionally independent set of…
Reduction to physical degrees of freedom before quantization leads to predictions for one-loop amplitudes in quantum cosmology in the presence of boundaries which disagree with the results obtained from Faddeev-Popov theory and…
It is shown that a simple modification of the dimensional regularization allows to compute in a consistent and gauge invariant way any diagram with less than four loops in the SO(10) unified model. The method applies also to the Standard…
We discuss conceptual aspects of renormalization in the context of effective field theories for the two-nucleon system. It is shown that, contrary to widespread belief, renormalization scheme dependence of the scattering amplitude can only…
Studies of geometrical theories suggest that fundmental problems of quantization arise from the disparate usage of displacement operators. These may be the source of a concealed inconsistency in the accepted formalism of quantum physics.…
We introduce an approach for calculating the quantum loop corrections in the $\phi^4$ theory. Differential regularization and background-field method are essential tools and are used to calculate the effective action of the theory to…
We extent the standard approach of dimensional regularization of Feynman diagrams: we replace the transition to lower dimensions by a 'natural' cut-off regulator. Introducing an external regulator of mass Lambda^(2e), we regain in the limit…
Using continuous wavelet transform it is possible to construct a regularization procedure for scale-dependent quantum field theory models, which is complementary to functional renormalization group method in the sense that it sums up the…
The quantization rules recently proposed by M. Navarro (and independently I.V. Kanatchikov) for a finite-dimensional formulation of quantum field theory are applied to the Klein-Gordon and the Dirac fields to obtain the quantum equations of…
Effective quantum field theories that allow for the possibility of Lorentz symmetry violation can sometimes also include redundancies of description in their Lagrangians. Explicit calculations in a Lorentz-violating generalization of Yukawa…