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- Ignazio Licata, Ammar Sakaji, A J Sakaji, Wai-Ning Mei, Richard Hammond, F K Diakonos +15 others
- 2009

General Relativity High energy laser interactions with charged particles Classical equation of motion with radiation reaction Electromagnetic radiation reaction forces Attilio Maccari Nonlinear phenomena, chaos and solitons in classic and quantum physics Technical Institute "G. Cardano" Via Alfredo Casella 3 00013 Mentana RM-ITALY Abstract: It is well known… (More)

- Tepper L Gill, W W Zachary
- 2001

In this paper, we provide a representation theory for the Feynman operator calculus. This allows us to solve the general initial-value problem and construct the Dyson series. We show that the series is asymptotic, thus proving Dyson's second conjecture for QED. In addition, we show that the expansion may be considered exact to any finite order by producing… (More)

- T L Gill, W W Zachary
- 2006

Let Ω be an open domain of class C 3 contained in R 3 , let (L 2 [Ω]) 3 be the real Hilbert space of square integrable functions on Ω with values in R 3 , and let H[Ω] be the completion of the set, ˘ u ∈ (C ∞ 0 [Ω]) 3 | ∇ · u = 0 ¯ , with respect to the inner product of (L 2 [Ω]) 3. A well-known unsolved problem is the construction of a sufficient class of… (More)

In this paper, we construct a parallel image of the conventional Maxwell theory by replacing the observer-time by the proper-time of the source. This formulation is mathematically, but not physically, equivalent to the conventional form. The change induces a new symmetry group which is distinct from, but closely related to the Lorentz group, and fixes the… (More)

- T L Gill, W W Zachary
- 2006

Let Ω be an open domain of class C 3 contained in R 3 , let (L 2 [Ω]) 3 be the real Hilbert space of square integrable functions on Ω with values in R 3 , and let D[Ω] = ˘ u ∈ (C ∞ 0 [Ω]) 3 | ∇ · u = 0 ¯. Let H[Ω] be the completion of D with respect to the inner product of (L 2 [Ω]) 3 and let V[Ω] be the completion of D[Ω] with respect to the inner product… (More)

- Tepper L Gill, W W Zachary
- 2005

In this paper, we provide an introduction to the theory of isotopes in infinite dimensional spaces. Although we consider this to be an introduction, most of the results a new, and have never appeared in print. We restrict ourselves to Hilbert spaces and develop the linear theory, providing detailed proofs for all major results. After a few examples, in the… (More)

- T L Gill, S Basu, W W Zachary, V Steadman
- 2003

In this paper we show that a result of Gross and Kuelbs, used to study Gaussian measures on Banach spaces, makes it possible to construct an adjoint for operators on separable Banach spaces. This result is used to extend well-known theorems of von Neumann and Lax. We also partially solve an open problem on the existence of a Markushevich basis with unit… (More)

- Tepper L Gill, W W Zachary
- 2003

In this paper, using the theory of fractional powers for operators, we construct the most general (analytic) representation for the square-root operator of relativistic quantum theory. We allow for arbitrary, but time-independent, vector potential and mass terms. Our representation is uniquely determined by the Green's function for the corresponding… (More)

- Tepper L Gill, Trey Morris, Stewart K Kurtz
- 2015

This paper is a progress report on the foundations for the canonical proper-time approach to relativistic quantum theory. We first review the the standard square-root equation of relativistic quantum theory, followed by a review of the Dirac equation, providing new insights into the physical properties of both. We then introduce the canonical proper-time… (More)

- Tepper L Gill, Marzett Golden
- 2015

The purpose of this note is to show that, if B is a uniformly convex Banach, then the dual space B has a " Hilbert space representation " (defined in the paper), that makes B much closer to a Hilbert space then previously suspected. As an application, we prove that, if B also has a Schauder basis (S-basis), then for each A ∈ C[B] (the closed and densely… (More)