Related papers: On conserved operator quantities in quantum field …
Linear response theory is concerned with the way in which a physical system reacts to a small change in the applied forces. Here we show that quantum mechanics in the Heisenberg representation can be understood as a linear response theory.…
Realistic dynamical theories of measurement based on the diffusion of quantum states are nonunitary, whereas quantum field theory and its generalizations are unitary. This problem in the quantum field theory of quantum state diffusion (QSD)…
Motivated by the sharp contrast between classical and quantum physics as probability theories, in these lecture notes I introduce the basic notions of operator algebras that are relevant for the algebraic approach to quantum physics.…
It is shown that the non-associative operators in a non-associative quantum theory are unobservables. The observable quantity may be presented only by the elements of some associative subalgebra. It is shown that the elements of the…
In this paper we demonstrate how the Legendre transform connects the statements of Noether's theorem in Hamiltonian and Lagrangian mechanics. We give precise definitions of symmetries and conserved quantities in both the Hamiltonian and…
We explore a wider theoretical framework that has quantum field theory built-in, taking the fact that quantum mechanics is reconstructed from quantum field theory as a hint. We formulate a quantum theory with an embedded structure by…
In Lagrangian mechanics, Noether conservation laws including the energy one are obtained similarly to those in field theory. In Hamiltonian mechanics, Noether conservation laws are issued from the invariance of the Poincare-Cartan integral…
Using the Noether Charge formulation, we study a perturbation of the conserved gravitating system. By requiring the boundary term in the variation of the Hamiltonian to depend only on the symplectic structure, we propose a general…
A geometric framework, called multicontact geometry, has recently been developed to study action-dependent field theories. In this work, we use this framework to analyze symmetries in action-dependent Lagrangian and Hamiltonian field…
In this paper, operator gauge transformation, first introduced by Kobe, is applied to Maxwell's equations and continuity equation in QED. The gauge invariance is satisfied after quantization of electromagnetic fields. Inherent nonlinearity…
Of crucial importance to the development of quantum computing and information has been the construction of a quantum operations formalism that admits a description of quantum noise while simultaneously revealing the behavior of an open…
These are notes on some entanglement properties of quantum field theory, aiming to make accessible a variety of ideas that are known in the literature. The main goal is to explain how to deal with entanglement when -- as in quantum field…
We define covariantly a deformation of a given algebra, then we will see how it can be related to a deformation quantization of a class of observables in Quantum Field Theory. Then we will investigate the operator order related to this…
Bohmian mechnaics is the most naively obvious embedding imaginable of Schr\"odingers's equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at…
Irreducibility of the set of quantum field operators has been proved in noncommutative quantum field theory in the general case when time does not commute with spatial variables.
A construction of conservation laws and conserved quantities for perturbations in arbitrary metric theories of gravity is developed. In an arbitrary field theory, with the use of incorporating an auxiliary metric into the initial Lagrangian…
The Lagrangian formalism for tensor fields over differentiable manifolds with contravariant and covariant affine connections (whose components differ not only by sign) and metrics [$(\bar{L}_n,g)$-spaces] is considered. The functional…
This paper expounds the relations between continuous symmetries and conserved quantities, i.e. Noether's ``first theorem'', in both the Lagrangian and Hamiltonian frameworks for classical mechanics. This illustrates one of mechanics' grand…
The Lagrangian formalism for variational problem for second-order delay ordinary differential equations (DODEs) is developed. The Noether-type operator identities and theorems for DODEs of second order are presented. Algebraic construction…
There is a large class of classical null-fronted metrics in which a free scalar field has an infinite number of conservation laws. In particular, if the scalar field is quantized, the number of particles is conserved. However, with more…