Related papers: Noether Theorem and the quantum mechanical operato…
We examine the assumptions behind Noether's theorem connecting symmetries and conservation laws. To compare classical and quantum versions of this theorem, we take an algebraic approach. In both classical and quantum mechanics, observables…
We clarify the relation between canonical and metric energy-momentum tensors. In particular, we show that a natural definition arises from Noether's Theorem which directly leads to a symmetric and gauge invariant tensor for electromagnetic…
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…
Noether's theorem has gained outstanding importance in theoretical particle physics, because it leads to basic conservation laws, such as the conservation of momentum and of angular momentum. Closely related to this theorem, but unnoticed…
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…
In this work, we investigate the structure and properties of the canonical energy momentum tensor (EMT) across a range of field theories. We begin by developing a unified and systematic method that naturally yields the canonical EMT for…
The long standing problem of the ordering ambiguity in the definition of the Hamilton operator for a point particle in curved space is naturally resolved by using the powerful geometric calculus based on Clifford Algebra. The momentum…
Methods of angular momenta are modified and used to solve some actual problems in quantum mechanics. In particular, we re-derive some known formulas for analytical and numerical calculations of matrix elements of the vector physical…
This is the first chapter of a new and unconventional textbook on quantum mechanics and quantum field theory. The chapter introduces standard quantum mechanics by means of a symmetry principle, without reference to classical mechanics. The…
We offer a clear physical explanation for the emergence of the quantum operator formalism, by revisiting the role of the vacuum field in quantum mechanics. The vacuum or random zero-point radiation field has been shown previously, using the…
It is shown that the quantum position operator of Newton and Wigner for non-zero mass systems is uniquely determined if one imposes a quantum ''manifest covariance'' condition of the same type as the similar condition of Currie, Jordan and…
In this initial paper in a series, we first discuss why classical motions of small particles should be treated statistically. Then we show that any attempted statistical description of any nonrelativistic classical system inevitably yields…
Despite the fact that it has been known since the time of Heisenberg that quantum operators obey a quantum version of Newton's laws, students are often told that derivations of quantum mechanics must necessarily follow from the Hamiltonian…
We consider in a quantum field theory framework the effects of a classical magnetic field on the spin and orbital angular momentum (OAM) of a free electron. We derive formulae for the changes in the spin and OAM due to the introduction of a…
A didatic approach of the Noether's theorem in classical mechanics is derived and used to obtain the laws of conservation.
A quantum field theory is described which is a supersymmetric classical model. -- Supersymmetry generators of the system are used to split its Liouville operator into two contributions, with positive and negative spectrum, respectively. The…
We consider algebras of quantum differential operators, for appropriate bicharacters on a polynomial algebra in one indeterminate and for the coordinate algebra of quantum $n$-space for $n\geq 3$. In the former case a set of generators for…
We study angular momentum in non-relativistic quantum electrodynamics (NRQED). We construct the effective total angular momentum operator by applying Noether's theorem to the NRQED lagrangian. We calculate the NRQED matching for the…
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…
The quantization of systems with a position dependent mass (PDM) is studied. We present a method that starts with the study of the existence of Killing vector fields for the PDM geodesic motion (Lagrangian with a PDM kinetic term but…