Negative Dimensional Integration. 2. Path Integrals and Fermionic Equivalence

Dunne, Gerald V.; Halliday, I.G.

doi:10.1016/0370-2693(87)91230-5

Negative Dimensional Integration. 2. Path Integrals and Fermionic Equivalence

Mar, 1987

14 pages

Published in:

Phys.Lett.B 193 (1987) 247

DOI:

10.1016/0370-2693(87)91230-5

Report number:

IMPERIAL/TP/86-87/10

View in:

reference search44 citations

Citations per year

Abstract: (Elsevier)

We present a working definition of negative dimensional integration which reduces the evaluation of integrals to the algebraic problem of resumming polynomial expressions. We demonstrate its equivalence to fermionic integration. Then we apply this to the calculation of Green's functions for the harmonic and anharmonic oscillators. Finally we comment on the connection between negative dimensional integration and Parisi-Sourlas supersymmetry.

QUANTUM MECHANICS: PATH INTEGRAL
MATHEMATICAL METHODS: DIMENSIONAL REDUCTION
MODEL: OSCILLATOR
FERMION
N-POINT FUNCTION
SUPERSYMMETRY

References(10)

Figures(0)

Random-Field Instability of the Ordered State of Continuous Symmetry

Yoseph Imry
(
- Brookhaven
)
,
Shang-keng Ma
(
- UC, San Diego
)

- Phys.Rev.Lett. 35 (1975) 1399-1401
•
DOI:
- 10.1103/PhysRevLett.35.1399

- J.Phys.C 10 L257

The Ising Model in a Random Field: Supersymmetric Surface Fluctuations and Their Implications in Three-dimensions

H.S. Kogon
(
- Edinburgh U.
)
,
D.J. Wallace
(
- Edinburgh U.
)

- J.Phys.A 14 (1981) L527
•
DOI:
- 10.1088/0305-4470/14/12/009

Random Magnetic Fields, Supersymmetry and Negative Dimensions

G. Parisi
(
- Frascati
)
,
N. Sourlas
(
- Ecole Normale Superieure
)

- Phys.Rev.Lett. 43 (1979) 744,
- IN *DAMGAARD, P.H. (ED.), HUEFFEL, H. (ED.): STOCHASTIC QUANTIZATION*, 199-200. (PHYS. REV. LETT. 43 (1979) 744-745) AND PARIS EC. NORM. SUP. - LPTENS 79-13 (79,REC.JUL.) 7 P. (SEE BOOK INDEX)
•
DOI:
- 10.1103/PhysRevLett.43.744

NONPERTURBATIVE EFFECTS IN A SCALAR SUPERSYMMETRIC THEORY

John L. Cardy
(
- UC, Santa Barbara
)

- Phys.Lett.B 125 (1983) 470-472
•
DOI:
- 10.1016/0370-2693(83)91328-X

Regularization and Renormalization of Gauge Fields

Gerard 't Hooft
(
- Utrecht U.
)
,
M.J.G. Veltman
(
- Utrecht U.
)

- Nucl.Phys.B 44 (1972) 189-213,
- Also in *Lai, C. H. ( Ed.): Gauge Theory Of Weak and Electromagnetic Interactions*, 322-346
•
DOI:
- 10.1016/0550-3213(72)90279-9

Gibbs Average in the Functional Formulation of Quantum Field Theory

Vittorio de Alfaro
(
- CERN
)
,
S. Fubini
(
- CERN
)
,
G. Furlan
(
- Trieste U. and
- INFN, Trieste and
- ICTP, Trieste
)

- Phys.Lett.B 105 (1981) 462-466
•
DOI:
- 10.1016/0370-2693(81)91205-3

- Phys.Lett.B 130 187

Propagators of quantized field

P.T. Matthews
(
- Birmingham U.
)
,
Abdus Salam
(
- Cambridge U.
)

- Nuovo Cim. 2 (1955) 120-134
•
DOI:
- 10.1007/BF02856011

The Grassmann Oscillator

R. Finkelstein
(
- UCLA
)
,
M. Villasante
(
- UCLA
)

- Phys.Rev.D 33 (1986) 1666
•
DOI:
- 10.1103/PhysRevD.33.1666