Abstract
Hamiltonian light-front dynamics of quantum fields may provide a useful approach to systematic nonperturbative approximations to quantum field theories. We investigate inequivalent Hilbert-space representations of the light-front field algebra in which the stability group of the light front is implemented by unitary transformations. The Hilbert space representation of states is generated by the operator algebra from the vacuum state. There is a large class of vacuum states besides the Fock vacuum which meet all the invariance requirements. The light-front Hamiltonian must annihilate the vacuum and have a positive spectrum. We exhibit relations of the Hamiltonian to the nontrivial vacuum structure.
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References
N. N. Bogolubovet al., General Principles of Quantum Theory (Kluwer Academic, Dordrecht, 1990), p. 262.
L. Van Hove,Physics 18, 145 (1952).
K. O. Friedrics,Mathematical Aspects of the Quantum Theory of Fields (Interscience, New York, 1953).
L. Gårding and A. S. Wightman,Proc. Natl. Acad. USA 40, 622 (1956).
I. E. Segal,Trans. Am. Math. Soc. 88, 12 (1958).
F. Coester and R. Haag,Phys. Rev. 117, 1137 (1960).
H. Araki,J. Math. Phys. 1, 492 (1964).
P. A. M. Dirac,Rev. Mod. Phys. 21, 329 (1949).
S. Weinberg,Phys. Rev. 150, 1313 (1966).
H. C. Pauli and S. J. Brodsky,Phys. Rev. D 32, 1993, 2001 (1985).
R. J. Perryet al., Phys. Rev. Lett. 65, 2959 (1990).
D. Mustakiet al., Phys. Rev. D 43, 3411 (1991).
A. C. Tanget al., Phys. Rev. D 44, 1842 (1991).
T. Maskawa and K. Yamawaki,Prog. Theor. Phys. 56, 270 (1976).
Th. Heinzlet al., Z. Phys. A 334, 443 (1989);Phys. Lett. B 256, 55 (1991);Nucl. Phys. A 532, 429c (1991); Regensburg Preprint TPR 92-17.
G. McCartor and D. Robertson,Z. Phys. C 53, 679 (1992).
S. Pinsky, Ohio State Preprint OHSTPY-HEP-TH-92-030.
F. Rohrlich,Acta Phys. Austriaca, Supp. 8, 277 (1971); see Sec. 5.
F. Coester,Prog. Nucl. Part. Phys. 29, 1 (1992).
H. Araki and E. J. Woods,J. Math. Phys. 4, 637 (1963).
S. Schlieder and E. Seiler,Commun. Math. Phys. 25, 62 (1972).
L. Schwartz,Théorie des Distributions (Hermann, Paris, 1957).
I. M. Gelfand and G. E. Shilov,Generalized Functions (Academic, New York, 1964).
R. Haag,Local Quantum Physics (Springer, New York, 1992).
R. F. Streater and A. S. Wightman,PCT, Spin & Statistics and All That (Benjamin, New York, 1964).
See Sec. II. 1.2, Ref. 24.
See Chap. III, Ref. 24.
H. Leutwyler, J. R. Klauder, and L. Streit,Nuovo Cimento A 66, 536 (1970).
N. Bourbaki,Lie Groups and Lie Algebras (Springer, New York, 1989), pp. 160–161.
See Sec. II.2.2, Ref. 24.
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Coester, F., Polyzou, W. Vacuum structures in Hamiltonian light-front dynamics. Found Phys 24, 387–400 (1994). https://doi.org/10.1007/BF02058099
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DOI: https://doi.org/10.1007/BF02058099