相关论文: Ward - Takahashi identities and Noether's theorem …

We consider self-interacting, perturbative quantum field theory in a curved spacetime background with a Killing vector field. We show that the action of this spacetime symmetry on interacting field operators can be implemented by a Noether…

We introduce the 3-colour noncommutative quantum field theory model in two dimensions. For this model we prove a generalised Ward-Takahashi identity, which is special to coloured noncommutative QFT models and has no underlying continuous…

The transition from a classical to quantum theory is investigated within the context of orthogonal and symplectic Clifford algebras, first for particles, and then for fields. It is shown that the generators of Clifford algebras have the…

Ward-Takahashi identities of the colored Boulatov model are derived using a generic unitary field transformation. In a specific instance, this generic transformation turns out to be a symmetry of the interaction so that particular classes…

Three major misconceptions concerning quantized tachyon fields: the energy spectrum unbounded from below, the frame-dependent and unstable vacuum state, and the non-covariant commutation rules, are shown to be a result of misrepresenting…

A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…

Consideration of the Noether variational problem for any theory whose action is invariant under global and/or local gauge transformations leads to three distinct theorems. These include the familiar Noether theorem, but also two equally…

We present a summary of the progress made in the last few years on topological quantum field theory in four dimensions. In particular, we describe the role played by duality in the developments which led to the Seiberg-Witten invariants and…

This paper presents a formulation of Noether's theorem for fractional classical fields. We extend the variational formulations for fractional discrete systems to fractional field systems. By applying the variational principle to a…

A theoretical study is made of conformal factors in certain types of physical theories based on classical differential geometry. Analysis of quantum versions of Weyl's theory suggest that similar field equations should be available in four,…

The theory of the calculus of variations for fuzzy systems was recently initiated in [7], with the proof of the fuzzy Euler-Lagrange equation. Using fuzzy Euler-Lagrange equation, we obtain here a Noether-like theorem for fuzzy variational…

Quantum field theory violates all the classical energy conditions of general relativity. Nonetheless, it turns out that quantum field theories satisfy remnants of the classical energy conditions, known as Quantum Energy Inequalities (QEIs),…

We study the equivalence principle and its violations by quantum effects in scalar-tensor theories that admit a conformal frame in which matter only couples to the spacetime metric. These theories possess Ward identities that guarantee the…

We take quantum theory and replace $\mathbb{C}$ by $\mathbb{C}[\varepsilon]$ where $\varepsilon^2=0$, i.e. we extend quantum theory to the ring of dual complex numbers. The aim is to develop a common language in which to treat continuous…

A general variational principle of classical fields with a Lagrangian containing the field quantity and its derivatives of up to the N-th order is presented. Noether's theorem is derived. The generalized Hamilton-Jacobi's equation for the…

For classical field theories with probabilistic initial conditions the classical field observables are an idealization. Their arbitrarily precise values poorly reflect the characteristic uncertainty in the presence of substantial…

Gravitational effective field theories with nondynamical backgrounds explicitly break diffeomorphism and local Lorentz invariance. At the same time, to maintain observer independence the action describing these theories is required to be…

There exists a paradox in quantum field theory: substituting a field configuration which solves a subset of the field equations into the action and varying it is not necessarily equivalent to substituting that configuration into the…

We reconsider the quantum analogue of Varadhans Theorem proved by Petz, Raggio and Verbeure. They proved this theorem using standard techniques in quantum statistical mechanics of lattice systems to arrive at a variational formula over…

In a recent formulation of a quantum field theory of forward rates, the volatility of the forward rates was taken to be deterministic. The field theory of the forward rates is generalized to the case of stochastic volatility. Two cases are…