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Luther Rinehart

Publications and source records attributed to Luther Rinehart.

6 recordsLinked to original sources
arXiv2022

Radiation from an accelerating charge in a family of Rindler frames

The generalization of the Larmor radiation formula in gravitational fields and with accelerating observers was obtained by Hirayama and others. We verify a special case of their result by explicit computation using a family of displaced Rindler frames. We discuss the role of observer-dependence of energy and simultaneity. We also include a discussion of conservation laws in spacetimes equipped with a Killing vector and a time function.

gr-qc↗
arXiv2022

Elliptic operators on non-compact manifolds have closed range

We show that a second-order elliptic differential operator $P$, on any manifold $M$, has closed range in $C^\infty(M)$. If $M$ has no compact components, then $P$ is surjective on $C^\infty(M)$. Applications to Helmholtz decomposition are discussed.

math.AP↗
arXiv2021

Eigenstates of C*-Algebras

We introduce the notion of eigenstate of an operator in an abstract C*-algebra, and prove several properties. Most significantly, if the operator is self-adjoint, then every element of its spectrum has a corresponding eigenstate.

math.OA↗
arXiv2015

Classical Fermionic Dynamics

The formulation of classical mechanics applicable to fermionic degrees of freedom is presented in mathematically rigorous terms, including a description of how the mathematical structure relates to the quantization of the theory. Canonical transformations and the algebra of observables are defined and studied. A formula is given for the analog of the Poisson bracket. The quantization of the theory proceeds according to deformation quantization.

math-ph↗
arXiv2015

Mathematical Foundations of Field Theory

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 formulations of field theory suffer greatly from either a failure to explicitly define the field configuration space, or else from the choice to define field operators as distributions. A solution to such problems is given by instead using locally square-integrable functions, and by paying close attention to this space's topology. One benefit of this is a clarification of the field multiplication problem: The pointwise product of fields is still not defined for all states, but it is densely defined, and this is shown to be sufficient for specifying dynamics. Significant progress is also made, through this choice of configuration space, in appropriately representing field states with `infinitely many particles', or those which do not go to zero at infinity.

math-ph↗