Related papers: Field Redefinitions in Classical Field Theory with…
The Hamiltonian approach to the quantum field theory is considered. Since there are additional difficulties such as the Haag theorem and Stueckelberg divergences, renormalization of the time-dependent dynamical quantum field theory is much…
A redefinition of the Lagrangian of a multi-particle system in fields reformulates the single-particle, kinetic, and fluid equations governing fluid and plasma dynamics as a single set of generalized Maxwell's equations and Ohm's law for…
We consider classical and quantum mechanics for an extended Heisenberg algebra with additional canonical commutation relations for position and momentum coordinates. In our approach this additional noncommutativity is removed from the…
A quantum scalar field theory with spacetime-dependent coupling is studied. Surprisingly, while translation invariance is explicitly broken in the classical theory, momentum conservation is recovered at the quantum level for some specific…
We revisit the lore establishing the allowed space of field redefinitions and show that there are essentially no restrictions. Our conclusions hold to all orders in perturbation theory and for any dispersion relation. Field redefinitions…
In this paper we introduce a geometric description of Lagrangian and Hamiltonian classical field theories on Lie algebroids in the framework of $k$-cosymplectic geometry. We discuss the relation between Lagrangian and Hamiltonian…
Finite element representations of Maxwell's equations pose unusual challenges inherent to the variational representation of the `curl-curl' equation for the fields. We present a variational formulation based on classical field theory.…
Theory of gravity is considered in the Regge-Teitelboim approach in which the pseudo-Riemannian space is treated as a surface isometrically embedded in an ambient Minkowski space of higher dimension. This approach is formulated in terms of…
By averaging over an ensemble of field configurations, a classical field theory can display many of the characteristics of quantum field theory, including Lorentz invariance, a loop expansion, and renormalization effects. There is…
We study classical field theories in a background field configuration where all modes of the theory are excited, matching the zero-point energy spectrum of quantum field theory. Our construction involves elements of a theory of classical…
Deterministic dynamical models are discussed which can be described in quantum mechanical terms. In particular, a local quantum field theory is presented which is a supersymmetric classical model. -- The Hilbert space approach of Koopman…
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…
The problem of renormalization of the semiclassical one-loop equations used in the non-equilibrium field theory is considered. Recently, the renormalizability of such equations has been justified for some special cases of classical field…
We review in simple terms the covariant approaches to the canonical formulation of classical relativistic field theories (in particular gauge field theories and general relativity) and we discuss the relationships between these approaches…
A nonlinear Wightman field is taken to be a nonlinear map from a linear space of test functions to a linear space of Hilbert space operators, with inessential modifications to other axioms only to the extent dictated by the introduction of…
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…
In contrast with QFT, classical field theory can be formulated in a strict mathematical way if one defines even classical fields as sections of smooth fiber bundles. Formalism of jet manifolds provides the conventional language of dynamic…
By employing special solutions of the Hamilton-Jacobi equation and tools from lattice theories, we suggest an approach to convert classical theories to quantum theories for mechanics and field theories. Some nontrivial results are obtained…
We have addressed the issue of field redefinition in connection with renormalisability. Our study is restricted to theories of interacting scalar fields. We have, in particular, shown that if a theory is renormalisable in the usual…
We study a class of perturbative scalar quantum field theories where dynamics is characterized by Lorentz-invariant or Lorentz-breaking non-local operators of fractional order and the underlying spacetime has a varying spectral dimension.…