2008

Unitarity, Lorentz invariance and causality in Lee-Wick theories: An asymptotically safe completion of QED

van Tonder, André

Understand

We revisit the previously unsolved problems of ensuring Lorentz invariance and non-perturbative unitarity in Lee-Wick theories.

We base our discussion on an ultraviolet completion of QED by Lee-Wick ghost fields, which is argued to be asymptotically safe.
We argue that as long as the state space is based upon a suitable choice of distributions of a type invented by Gel'fand and Shilov, the Lee-Wick ghosts can be eliminated while preserving Lorentz invariance to produce a unitary theory.
The method for eliminating ghosts is in principle non-perturbatively well-defined, in contrast with some previous proposals.

N.N. Bogolubov, A.A. Logunov, A.I. Oksak and I.T. Todorov, General principles of quantum field theory
Original
1929
Earlier work this paper cites.
W. Pauli and F. Villars, On the invariant regularization in relativistic quantum field theory
1949
Earlier work this paper cites.
I.M Gel’fand and G.E. Shilov, Generalized functions: Spaces of fundamental and generalized functions
1958
Earlier work this paper cites.
Roger, G. Newton, Analytic properties of radial wave functions
1960
Earlier work this paper cites.
A.I. Mal’cev, Foundations of linear algebra
1963
Earlier work this paper cites.
I.M Gel’fand and G.E. Shilov, Generalized functions: Theory of differential equations
1967
Earlier work this paper cites.
Tore Berggren, On the use of resonant states in eigenfunction expansions of scattering and reaction amplitudes
1968
Earlier work this paper cites.
T.D. Lee and G.C. Wick, Negative metric and the unitarity of the S-matrix
1969
Earlier work this paper cites.
R.E. Cutkosky, P.V. Landshoff, D.I. Olive and J.C. Polkinghorne, Nuclear Physics
1969
Earlier work this paper cites.
T.D. Lee, A relativistic complex pole model with indefinite metric
1970
Earlier work this paper cites.
S. Coleman, Acausality
1970
Earlier work this paper cites.

T.D. Lee, A finite theory of quantum electrodynamics
1971
Cited alongside, same era.
N. Nakanishi, Lorentz noninvariance of the complex-ghost relativistic field theory
1971
Cited alongside, same era.
N. Nakanishi, Remarks on the complex-ghost relativistic field theory
1971
Cited alongside, same era.
A.M. Gleeson, R.J. Moore, H. Rechtenberg, and E.C.G. Sudarshan, Analyticity, covariance, and unitarity in indefinite-metric quantum field theories
1971
Cited alongside, same era.
J. Bognár, Indefinite inner product spaces
1974
Cited alongside, same era.
K.S. Stelle, Renormalization of higher-derivative quantum gravity
1977
Cited alongside, same era.
S. Weinberg, in General Relativity
1979
Cited alongside, same era.
C. Itzykson, J.-B. Zuber, Quantum Field Theory
1980
Cited alongside, same era.
Y.K. Ho, The method of complex coordinate rotation and its application to atomic collision processes
1983
Cited alongside, same era.
D.G. Boulware and D.G. Gross, Lee-Wick indefinite metric quantization: A functional integral approach
1984
Cited alongside, same era.
A. Buchleitner, B. Grémaud and D. Delande, Wavefunctions of atomic resonances
1994
Cited alongside, same era.
Thomas G. Rizzo, Searching for Lee-Wick Gauge Bosons at the LHC
Original
Cited in the paper.

Nimrod Moiseyev, Quantum theory of resonances: calculating energies, widths and cross-sections by complex scaling
1998
Later among the works it cites.
Joseph Polchinski, Leonard Susskind, Nicolaos Toumbas, Negative Energy, Superluminosity and Holography
1999
Later among the works it cites.
Leonard Susskind, Nicolaos Toumbas, Wilson Loops as Precursors
2000
Later among the works it cites.
Gary T. Horowitz, Juan Maldacena, The black hole final state
2004
Later among the works it cites.
G. Hagen, J.S. Vaagen and M. Hjort-Jensen, The contour deformation method in momentum space, applied to subatomic physics
2004
Later among the works it cites.
Carl M. Bender, Sebastian F. Brandt, Jun-Hua Chen, Qinghai Wang, Physical Review
2005
Later among the works it cites.
R. de la Madrid, Description of resonances within the rigged Hilbert space
2006
Later among the works it cites.
B. Grinstein, D. O’Connell, M.B. Wise, The Lee-Wick Standard Model
2008
Closest in time.
Jose Ramon Espinosa, Benjamin Grinstein, Donal O’Connell, Mark B. Wise, Neutrino Masses in the Lee-Wick Standard Model
2008
Closest in time.
Timothy R. Dulaney, Mark B. Wise, Flavor Changing Neutral Currents in the Lee-Wick Standard Model
2008
Closest in time.

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