Causality, unitarity, and indefinite metric in Maxwell-Chern-Simons extensions

Avila, Ricardo; Nascimento, Jose R.; Petrov, Albert Yu; Reyes, Carlos M.; Schreck, Marco

doi:10.1103/PhysRevD.101.055011

Causality, unitarity, and indefinite metric in Maxwell-Chern-Simons extensions

Nov 27, 2019

27 pages

Published in:

Phys.Rev.D 101 (2020) 5, 055011

Published: Mar 6, 2020

e-Print:

1911.12221 [hep-th]

DOI:

10.1103/PhysRevD.101.055011

View in:

reference search11 citations

Citations per year

Abstract: (APS)

We canonically quantize (2+1)-dimensional electrodynamics including a higher-derivative Chern-Simons term. The effective theory describes a standard photon and an additional degree of freedom associated with a massive ghost. We find the Hamiltonian and the algebra satisfied by the field operators. The theory is characterized by an indefinite metric in the Hilbert space that brings up questions on causality and unitarity. We study both of the latter fundamental properties and show that microcausality as well as perturbative unitarity up to one-loop order are conserved when the Lee-Wick prescription is employed.

Note:

New version published in PRD, Lee-Wick prescription in Sec. IV-C, 27 pages, 5 figures

Beyond the standard model
derivative: high
unitarity: violation
ghost: massive
indefinite metric
conservation law
Hilbert space
causality
electromagnetic field
Chern-Simons term

References(60)

Figures(5)

[1]

P.A.M. Dirac

- Proc.Roy.Soc.Lond.A 180 (1942) 1
•
DOI:
- 10.1098/rspa.1942.0023

[2]

Aspects of Quantum Theory

A. Salam
,
E.P. Wigner

[3]

Proceedings of the 1958 Annual International Conference on High Energy Physics at CERN, Geneva, 1958

B. Ferretti
,
W. Heisenberg

[4]

W. Pauli

- Rev.Mod.Phys. 15 (1943) 175
•
DOI:
- 10.1103/RevModPhys.15.175

[5]

Renormalization of Higher Derivative Quantum Gravity

K.S. Stelle
(
- Brandeis U.
)

- Phys.Rev.D 16 (1977) 953-969
•
DOI:
- 10.1103/PhysRevD.16.953

[6]

Indefinite metric quantum field theory

Noboru Nakanishi
(
- Kyoto U., RIMS
)

- Prog.Theor.Phys.Suppl. 51 (1972) 1-95
•
DOI:
- 10.1143/PTPS.51.1

[7]

Indefinite-Metric Quantum Field Theory of General Relativity

Noboru Nakanishi
(
- Kyoto U., RIMS
)

- Prog.Theor.Phys. 59 (1978) 972
•
DOI:
- 10.1143/PTP.59.972

[8]

Negative Metric and the Unitarity of the S Matrix

T.D. Lee
(
- CERN
)
,
G.C. Wick
(
- Columbia U.
)

- Nucl.Phys.B 9 (1969) 209-243,
- In *Lee, T.D.: Selected papers, vol. 2*, 83-117
•
DOI:
- 10.1016/0550-3213(69)90098-4

[9]

Finite Theory of Quantum Electrodynamics

T.D. Lee
(
- Columbia U.
)
,
G.C. Wick
(
- Columbia U.
)

- Phys.Rev.D 2 (1970) 1033-1048,
- In *Lee, T.D.: Selected papers, vol. 2*, 129-144, and Columbia Univ. New York - NYO-1932(2)-169 (rec.May 70) 64 p. (see Book Index)
•
DOI:
- 10.1103/PhysRevD.2.1033

[10]

Exploring Lee-Wick finite electrodynamics

Antonio Accioly
(
- Rio de Janeiro, CBPF and
- Sao Paulo State U.
)
,
Patricio Gaete
(
- Santa Maria U., Valparaiso and
- CCTVal, Valparaiso
)
,
Jose Helayel-Neto
(
- Rio de Janeiro, CBPF
)
,
Eslley Scatena
(
- Sao Paulo State U.
)
,
Rodrigo Turcati
(
- Rio de Janeiro, CBPF
)

e-Print:
- 1012.1045

[11]

A non-analytic S matrix

R.E. Cutkosky
(
- Cambridge U., DAMTP
)
,
P.V. Landshoff
(
- Cambridge U., DAMTP
)
,
David I. Olive
(
- Cambridge U., DAMTP
)
,
J.C. Polkinghorne
(
- Cambridge U., DAMTP
)

- Nucl.Phys.B 12 (1969) 281-300
•
DOI:
- 10.1016/0550-3213(69)90169-2

[12]

The Lee-Wick standard model

Benjamin Grinstein
(
- UC, San Diego
)
,
Donal O'Connell
(
- Caltech
)
,
Mark B. Wise
(
- Caltech
)

- Phys.Rev.D 77 (2008) 025012
•
e-Print:
- 0704.1845
•
DOI:
- 10.1103/PhysRevD.77.025012

[13]

A new formulation of Lee-Wick quantum field theory

Damiano Anselmi
(
- INFN, Pisa and
- Pisa U.
)
,
Marco Piva
(
- INFN, Pisa and
- Pisa U.
)

- JHEP 06 (2017) 066
•
e-Print:
- 1703.04584
•
DOI:
- 10.1007/JHEP06(2017)066

[14]

Perturbative unitarity of Lee-Wick quantum field theory

Damiano Anselmi
(
- Pisa U. and
- INFN, Pisa
)
,
Marco Piva
(
- Pisa U. and
- INFN, Pisa
)

- Phys.Rev.D 96 (2017) 4, 045009
•
e-Print:
- 1703.05563
•
DOI:
- 10.1103/PhysRevD.96.045009

[15]

About the triviality of the higher derivative sector in the abelian Lee-Wick model

- Braz.J.Phys. 48 (2018) 6, 619-628
•
e-Print:
- 1605.09339
•
DOI:
- 10.1007/s13538-018-0598-0

[16]

Super-renormalizable Quantum Gravity

Leonardo Modesto
(
- Perimeter Inst. Theor. Phys.
)

- Phys.Rev.D 86 (2012) 044005
•
e-Print:
- 1107.2403
•
DOI:
- 10.1103/PhysRevD.86.044005

[17]

Super-renormalizable or finite Lee–Wick quantum gravity

Leonardo Modesto
(
- Fudan U.
)

- Nucl.Phys.B 909 (2016) 584-606
•
e-Print:
- 1602.02421
•
DOI:
- 10.1016/j.nuclphysb.2016.06.004

[18]

Cutkosky rules and perturbative unitarity in Euclidean nonlocal quantum field theories

- Phys.Rev.D 99 (2019) 10, 104043
•
e-Print:
- 1803.08827
•
DOI:
- 10.1103/PhysRevD.99.104043

[19]

Making sense of non-Hermitian Hamiltonians

Carl M. Bender
(
- LANL, Ctr. for Nonlinear Studies
)

- Rept.Prog.Phys. 70 (2007) 947
•
e-Print:
- hep-th/0703096
•
DOI:
- 10.1088/0034-4885/70/6/R03

[20]

Minimal length in Quantum Mechanics and non-Hermitian Hamiltonian systems

- Phys.Lett.A 373 (2009) 4307-4310
•
e-Print:
- 0907.5354
•
DOI:
- 10.1016/j.physleta.2009.09.054

[21]

Gauge invariance and the Englert-Brout-Higgs mechanism in non-Hermitian field theories

Jean Alexandre
(
- King's Coll. London
)
,
John Ellis
(
- King's Coll. London and
- NICPB, Tallinn and
- CERN
)
,
Peter Millington
(
- Nottingham U.
)
,
Dries Seynaeve
(
- King's Coll. London
)

- Phys.Rev.D 99 (2019) 7, 075024
•
e-Print:
- 1808.00944
•
DOI:
- 10.1103/PhysRevD.99.075024

[22]

Some remarks on high derivative quantum gravity

M. Asorey
(
- Zaragoza U.
)
,
J.L. Lopez
(
- Zaragoza U.
)
,
I.L. Shapiro
(
- Zaragoza U. and
- Juiz de Fora U.
)

- Int.J.Mod.Phys.A 12 (1997) 5711-5734
•
e-Print:
- hep-th/9610006
•
DOI:
- 10.1142/S0217751X97002991

[23]

Living with ghosts

- Phys.Rev.D 65 (2002) 103515
•
e-Print:
- hep-th/0107088
•
DOI:
- 10.1103/PhysRevD.65.103515

[24]

The Problem of Nonlocality in String Theory

D.A. Eliezer
(
- UC, Santa Barbara
)
,
R.P. Woodard
(
- Brown U.
)

- Nucl.Phys.B 325 (1989) 389,
- NUCL. PHYS. B325 (1989) 389-469 AND CALIF. UNIV. SANTA BARBARA - UCSB-TH-89-09 (89,REC.APR.) 106 P. (906859)
•
DOI:
- 10.1016/0550-3213(89)90461-6

[25]

Living with ghosts and their radiative corrections

I. Antoniadis
(
- CERN and
- Ecole Polytechnique, CPHT
)
,
E. Dudas
(
- CERN and
- Ecole Polytechnique, CPHT and
- Orsay, LPT
)
,
D.M. Ghilencea
(
- Oxford U.
)

- Nucl.Phys.B 767 (2007) 29-53
•
e-Print:
- hep-th/0608094
•
DOI:
- 10.1016/j.nuclphysb.2006.12.019

1-25 of 60
1
2
3
25 / page