- Email: [email protected]
Supersymmetric gauge theories in quantum mechanics
ANNALS OF PHYSICS 162. 228-229
Abstracts
(1985)
of Papers
Supersymmefric Gauge Theories sitlt Bonn, West Germany;
to Appear
in Quantum Mechanics. AND S. YANKIELOWICZ,
in Future
V. RITTENBERG, Physikalisches Institut, UniverTel-Aviv University, Ramat-Aviv, Israel.
A general construction for supersymmetric (i( 1) gauge invariant Hamiltonians is given. For a given number of fermionic and bosonic degrees of freedom it supercharges the interactions are determined uniquely, and coincide with the N = 1, d= 3 + I supersymmetric electrodynamics. If there are two supercharges cannot be obtained through dimensional reduction. For two special choices of sionally reduced d= I + 1 Weyl supersymmetric and Majorana supersymmetric found.
The Casimir Brighton
Effect with BNl 9QH,
Finite-Muss England.
Photons.
G.
Issues
BARTON
AND N.
DOMBEY.
in quantum mechanics is shown that for four dimensionally reduced one gets models which a parameter the dimenelectrodynamics are
University
of Sussex,
The force between two perfectly conducting parallel slabs, each of width N, and separated by a distance 2L is calculated, using the Proca equations, which are appropriate when the photon has a tinite mass tn. The approach is through the L-dependence of the combined quantum zero-point energies (ZPE) of all the normal modes of the system. The general results are evaluated in a regime with 1= mL< 1 and v =mNe 1. The two leading finite-mass corrections are of relative order i.’ and A4 log A; both stem from essentially kinematic corrections to the modes already present in the Maxwell case m = 0, and having a discrete spectrum between the slabs. There are further corrections of relative order A4 and (for N+L) 6“ log(N/L), the last stemming from dynamically new (penetrating) modes present only for m#O, to which even perfect conductors are almost transparent, and which possess a continuous spectrum. The calculation has byproducts which may prove more fruitful than the results themselves. These are: (i) A complete analysis of the Proca normal-mode structure for parallel-plane geometry, the first such complete analysis, as far as we know, for any system. A special role is played by the component A, of the vector potential normal to the slabs, which is unique amongst the potentials and fields in that not only A, but also aAz/al are continuous across the surfaces; this governs the classification of the modes, and effectively reduces the analysis of the penetrating modes to that for a scalar field. (ii) A clearer understanding of the way in which the total ZPE of continuum modes varies with system parameters like L and N. (iii) Requisite for (ii), a statement of Levinson’s theorem in one dimension, which for evenparity modes displays unfamiliar features.
Classical Solutions IO Topologically Massive Yang-Mills Theory. ERIC D’HOKER, Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139; AND Luc VINET, Laboratoire de Physique Nucleaire. Universite de Montreal, Montreal, Quebec H3C3J7, Canada. Classical solutions to 2 + 1 dimensional Yang-Mills theory in the presence of the Chern-Simons invariant are considered. The S0(3)-invariant solutions to the Euclidean field equations are complex, whereas the equations in Minkowski space-time possess real SO(2, l)-invariant solutions. The field equations for time independent axially symmetric vector potentials are derived and some solutions are obtained. The behavior of general Euclidean space-time solutions is discussed. It is also shown that,
228 ooO3-4916/85 CopyrIght All rghts
$7.50
(0 1985 by of reproduction
Academic in any
Press, lorm
Inc. reserved.
Abstracts
(1985)
of Papers
Supersymmefric Gauge Theories sitlt Bonn, West Germany;
to Appear
in Quantum Mechanics. AND S. YANKIELOWICZ,
in Future
V. RITTENBERG, Physikalisches Institut, UniverTel-Aviv University, Ramat-Aviv, Israel.
A general construction for supersymmetric (i( 1) gauge invariant Hamiltonians is given. For a given number of fermionic and bosonic degrees of freedom it supercharges the interactions are determined uniquely, and coincide with the N = 1, d= 3 + I supersymmetric electrodynamics. If there are two supercharges cannot be obtained through dimensional reduction. For two special choices of sionally reduced d= I + 1 Weyl supersymmetric and Majorana supersymmetric found.
The Casimir Brighton
Effect with BNl 9QH,
Finite-Muss England.
Photons.
G.
Issues
BARTON
AND N.
DOMBEY.
in quantum mechanics is shown that for four dimensionally reduced one gets models which a parameter the dimenelectrodynamics are
University
of Sussex,
The force between two perfectly conducting parallel slabs, each of width N, and separated by a distance 2L is calculated, using the Proca equations, which are appropriate when the photon has a tinite mass tn. The approach is through the L-dependence of the combined quantum zero-point energies (ZPE) of all the normal modes of the system. The general results are evaluated in a regime with 1= mL< 1 and v =mNe 1. The two leading finite-mass corrections are of relative order i.’ and A4 log A; both stem from essentially kinematic corrections to the modes already present in the Maxwell case m = 0, and having a discrete spectrum between the slabs. There are further corrections of relative order A4 and (for N+L) 6“ log(N/L), the last stemming from dynamically new (penetrating) modes present only for m#O, to which even perfect conductors are almost transparent, and which possess a continuous spectrum. The calculation has byproducts which may prove more fruitful than the results themselves. These are: (i) A complete analysis of the Proca normal-mode structure for parallel-plane geometry, the first such complete analysis, as far as we know, for any system. A special role is played by the component A, of the vector potential normal to the slabs, which is unique amongst the potentials and fields in that not only A, but also aAz/al are continuous across the surfaces; this governs the classification of the modes, and effectively reduces the analysis of the penetrating modes to that for a scalar field. (ii) A clearer understanding of the way in which the total ZPE of continuum modes varies with system parameters like L and N. (iii) Requisite for (ii), a statement of Levinson’s theorem in one dimension, which for evenparity modes displays unfamiliar features.
Classical Solutions IO Topologically Massive Yang-Mills Theory. ERIC D’HOKER, Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139; AND Luc VINET, Laboratoire de Physique Nucleaire. Universite de Montreal, Montreal, Quebec H3C3J7, Canada. Classical solutions to 2 + 1 dimensional Yang-Mills theory in the presence of the Chern-Simons invariant are considered. The S0(3)-invariant solutions to the Euclidean field equations are complex, whereas the equations in Minkowski space-time possess real SO(2, l)-invariant solutions. The field equations for time independent axially symmetric vector potentials are derived and some solutions are obtained. The behavior of general Euclidean space-time solutions is discussed. It is also shown that,
228 ooO3-4916/85 CopyrIght All rghts
$7.50
(0 1985 by of reproduction
Academic in any
Press, lorm
Inc. reserved.