The Vacuum of (QED)0+1 and Functional Integral Measure with Boundary Conditions

After reviewing the basic aspects of the exactly solvable quantum-corrected dilaton gravity theories in two dimensions, we discuss a (subjective) selection of other aspects: (a) supersymmetric extensions, (b) the canonical formalism, ADM mass and the functional integral measure, and (c) a positive energy theorem and its application to the ADM and Bondi masses.

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Casimir effect for the scalar field under Robin boundary conditions: a functional integral approach

Journal of Physics A General Physics ◽

10.1088/0305-4470/37/27/012 ◽

2004 ◽

Vol 37 (27) ◽

pp. 7039-7050 ◽

Cited By ~ 23

Author(s):

Luiz C de Albuquerque ◽

R M Cavalcanti

Keyword(s):

Scalar Field ◽

Boundary Conditions ◽

Casimir Effect ◽

Functional Integral ◽

Integral Approach ◽

Robin Boundary Conditions ◽

Robin Boundary

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FUNCTIONAL INTEGRAL METHODS FOR FERMIONIC STRING AND SUPER RIEMANN SURFACES

International Journal of Modern Physics A ◽

10.1142/s0217751x89000923 ◽

1989 ◽

Vol 04 (09) ◽

pp. 2283-2315 ◽

Cited By ~ 1

Author(s):

KEN-JI HAMADA ◽

MASARU TAKAO

Keyword(s):

Light Cone ◽

Riemann Surfaces ◽

Functional Integral ◽

Light Cone Gauge ◽

Spin Structures ◽

Integral Methods ◽

Integral Measure ◽

Fermionic String ◽

Super Riemann Surfaces ◽

The One

We investigate the light-cone gauge formulation of fermionic string of Mandelstam in a superspace. To formulate the fermionic string in a superspace, we use the theory of super Riemann surfaces (SRS). We define the Neumann functions and the Mandelstam mappings in a superspace by means of the so-called Abelian differentials of the first and the third kinds on SRS. In the super Schottky parametrization of SRS these superdifferentials are constructed at the multiloop level. The functional integral measure of a super light-cone diagram, which consists of 6g−6+2N even moduli parameters and 4g−4+2N odd ones, are specified in our formulation. In one-loop case with even spin structures we explicitly evaluate the superdeterminants on the super light-cone diagrams and calculate the one-loop amplitudes with N massless vector states. It is shown that the result is written in the form of a correlation function of the vertex operators. Furthermore, we evaluate the 3- and 4-particle amplitudes explicitly, which agree exactly with those calculated in the Green-Schwarz formulation.

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Use of the Magnetostatic Analogue In Electromagnetic Lens Engineering

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100068795 ◽

1970 ◽

Vol 28 ◽

pp. 360-361

Author(s):

John W. Coleman

Keyword(s):

Boundary Conditions ◽

High Performance ◽

Force Fields ◽

Optical Design ◽

Direct Conversion ◽

Design Engineering ◽

Design Data ◽

Scalar Potentials ◽

Geometric Elements ◽

At Will

In the design engineering of high performance electromagnetic lenses, the direct conversion of electron optical design data into drawings for reliable hardware is oftentimes difficult, especially in terms of how to mount parts to each other, how to tolerance dimensions, and how to specify finishes. An answer to this is in the use of magnetostatic analytics, corresponding to boundary conditions for the optical design. With such models, the magnetostatic force on a test pole along the axis may be examined, and in this way one may obtain priority listings for holding dimensions, relieving stresses, etc..The development of magnetostatic models most easily proceeds from the derivation of scalar potentials of separate geometric elements. These potentials can then be conbined at will because of the superposition characteristic of conservative force fields.

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