相关论文: A mathematical base for Fibre bundle formulation o…
Despite the importance of the path integral, there have been relatively few attempts to look to the Lagrangian for a more realistic framework that might underlie quantum theory. While such realism is not available for the standard path…
In the present paper we propose a new approach to quantum fields in terms of category algebras and states on categories. We define quantum fields and their states as category algebras and states on causal categories with partial involution…
Hyperbolic lattices underlie a new form of quantum matter with potential applications to quantum computing and simulation and which, to date, have been engineered artificially. A corresponding hyperbolic band theory has emerged, extending…
The formalism of quantum mechanics is presented in a way that its interpretation as a classical field theory is emphasized. Two coupled real fields are defined with given equations of motion. Densities and currents associated to the fields…
In the context of Covariant Quantum Mechanics for a spin particle, we classify the ``quantum vector fields'', i.e. the projectable Hermitian vector fields of a complex bundle of complex dimension 2 over spacetime. Indeed, we prove that the…
The geometric Lagrangian theory (of arbitrary order) is based on the analysis of some basic mathematical objects such as: the contact ideal, the (exact) variational sequence, the existence of Euler-Lagrange and Helmholtz-Sonin forms, etc.…
We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one but it is in harmony with the modern trends in theoretical physics and potentially admits…
In this paper, we develop a general framework of geometric functorial field theories, meaning that all bordisms in question are endowed with geometric structures. We take particular care to establish a notion of smooth variation of such…
This paper gives an introduction to certain classical physical theories described in the context of locally Minkowskian causal structures (LMCSs). For simplicity of exposition we consider LMCSs which have locally Euclidean topology (i.e.…
Higgs fields are attributes of classical gauge theory on a principal bundle $P\to X$ whose structure Lie group $G$ if is reducible to a closed subgroup $H$. They are represented by sections of the quotient bundle $P/H\to X$. A problem lies…
We consider classical gauge theory on a principal bundle P->X in a case of spontaneous symmetry breaking characterized by the reduction of a structure group G of P->X to its closed subgroup H. This reduction is ensured by the existence of…
In modern physics, one of the greatest divides is that between space-time and quantum fields, as the fiber bundle of the Standard Model indicates. However on the operational grounds the fields and spacetime are not very different. To…
The mathematical formalism for linear quantum field theory on curved spacetime depends in an essential way on the assumption of global hyperbolicity. Physically, what lie at the foundation of any formalism for quantization in curved…
Present-day quantum field theory can be regularized by a decomposition into quantum simplices. This replaces the infinite-dimensional Hilbert space by a high-dimensional spinor space and singular canonical Lie groups by regular spin groups.…
A mathematically rigorous Hamiltonian formulation for classical and quantum field theories is given. New results include clarifications of the structure of linear fields, and a plausible formulation for nonlinear fields. Many mathematical…
Richard Borcherds proposed an elegant geometric version of renormalized perturbative quantum field theory in curved spacetimes, where Lagrangians are sections of a Hopf algebra bundle over a smooth manifold. However, this framework looses…
We attempt a clarification of geometric aspects of quantum field theory by using the notion of smoothness introduced by Fr\"olicher and exploited by several authors in the study of functional bundles. A discussion of momentum and position…
We formulate semi-classical field theory as an approximate decoherence-free-subspace of a finite-dimensional quantum-gravity hilbert space. A complementarity construction can be realized as a unitary transformation which changes the…
The author exposes the metrical multi-time Lagrange geometry of physical fields which naturally generalizes the classical Lagrangian developped by Miron and Anastasiei. In other words, one constructs a natural theory of physical fields on…
Algebraic quantum field theory is considered from the perspective of the Hochschild cohomology bicomplex. This is a framework for studying deformations and symmetries. Deformation is a possible approach to the fundamental challenge of…