Note on symmetry operations in quantum mechanics

Hagedorn, Rolf

doi:10.1007/bf02726536

Cited by 267 publications

(420 citation statements)

References 2 publications

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“…The temperature deduced from the fits is very close to the critical value for a QGP-to-hadron-gas transition predicted by Lattice QCD (T C = 175 MeV), but is also close to the Hagedorn limit for a hadron resonance gas, predicted without any consideration of quark and gluon degrees of freedom [42]. If thermalization is indeed achieved by the bulk matter prior to chemical freezeout, then the deduced value of T ch represents a lower limit on that thermalization temperature.…”

Section: Particle Yields and Chemical Freezeoutsupporting

confidence: 76%

Where are we in the search for the Quark Gluon Plasma?

Ullrich¹

2006

AIP Conference Proceedings

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The Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory was completed in 1999, with the first data-taking runs in the summer of 2000. Since then the measurements at RHIC have yielded a wealth of data from four independent detectors: BRAHMS, PHENIX, PHOBOS, and STAR. For the first time, collisions of heavy nuclei have been carried out with colliding-beam energies that have previously been accessible only to high-energy physics experiments. It is at these high energies that the predictions of QCD come into play and new phenomena are sought that may illuminate our view of the basic structure of matter.The RHIC experiments have recorded data from collisions of gold nuclei from Ô s NN 19 GeV up to the highest energy of 200 GeV, as well as reference data in proton-proton and deuteron-gold collisions. These collisions result in final states of unprecedented complexity, with thousands of produced particles radiating from the nuclear collision.The early measurements have revealed compelling evidence for the existence of a new form of nuclear matter at extremely high density and temperature. This medium allows for the predictions of QCD to be tested, and new phenomena explored, under conditions where the relevant degrees of freedom, over nuclear volumes, are expected to be those of quarks and gluons, rather than of hadrons. This is the realm of the quark gluon plasma.However, detailed analyses of the data also make it clear that this hot, dense medium has properties that are surprising, and not yet fully understood in terms of the early expectations for the quark gluon plasma. In this paper I review the major findings of the RHIC experiments to date and discuss the current understanding of the state of matter created.

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Section: Particle Yields and Chemical Freezeoutsupporting

confidence: 76%

Where are we in the search for the Quark Gluon Plasma?

Ullrich¹

2006

AIP Conference Proceedings

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“…Physical pure states correspond one-to-one to normalised or unit rays (i.e., to one-dimensional projections or density matrices). So we define 2) and call it the ray space. For finite N , R has real even dimension 2(N − 1).…”

Section: Notational Preliminaries Statement Of the Problemmentioning

confidence: 99%

“…[2]- [28]. Prominent among these is a proof by Bargmann in 1964 [6] which is extremely elegant and, in a sense, elementary.…”

Section: Introductionmentioning

confidence: 99%

Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics

et al. 2008

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In quantum theory, symmetry has to be defined necessarily in terms of the family of unit rays, the state space. The theorem of Wigner asserts that a symmetry so defined at the level of rays can always be lifted into a linear unitary or an antilinear antiunitary operator acting on the underlying Hilbert space. We present two proofs of this theorem which are both elementary and economical. Central to our proofs is the recognition that a given Wigner symmetry can, by post-multiplication by a unitary symmetry, be taken into either the identity or complex conjugation. Our analysis involves a judicious interplay between the effect a given Wigner symmetry has on certain two-dimensional subspaces and the effect it has on the entire Hilbert space.

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“…Despite these considerations some mathematicians, perhaps feeling that linearity is a natural concept and conjugate linearity an arti® ce, have tended to ignore the latter (see, for example, [4], pp. 82± 83; [5], p. 10).…”

Section: Introductionmentioning

confidence: 98%

A perspective on the relevance of com plex num bers and conjugate linearity

Almeida¹

1999

International Journal of Mathematical Education in Science and

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Note on symmetry operations in quantum mechanics

Cited by 267 publications

References 2 publications

Where are we in the search for the Quark Gluon Plasma?

Where are we in the search for the Quark Gluon Plasma?

Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics

A perspective on the relevance of com plex num bers and conjugate linearity

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