scholarly journals Bose and Fermi statistics and the regularization of the nonrelativistic Jacobian for the scale anomaly

2016 ◽  
Vol 94 (8) ◽  
Author(s):  
Chris L. Lin ◽  
Carlos R. Ordóñez
Keyword(s):  
Fermi Statistics

scholarly journals On the theory of heavy electrons and nuclear forces

1938 ◽  
Vol 166 (927) ◽  
pp. 501-528 ◽  
Keyword(s):  
Experimental Evidence ◽  
Rest Mass ◽  
High Energy ◽  
Electronic Charge ◽  
Nuclear Forces ◽  
Fermi Statistics ◽  
Heavy Electron ◽  
Very High Energy ◽  
Very High ◽  
Spin And Statistics

The view has been expressed by several authors, including Neddermeyer and Anderson (1937), and Street and Stevenson (1937 a, b ), that the penetrating component of cosmic radiation consists largely of new particles of electronic charge and mass intermediate between those of the electron and proton, and I have shown in a recent paper (Bhabha 1938 a ) that the shape of experimentally well-established facts, also necessitate such a particle and are not compatible with a breakdown of the theory for electrons of very high energy. It has further been shown in the same paper that it does not seem to be sufficient just to postulate another particle behaving exactly like an electron of larger mass, but that the experimental evidence demands further that under certain circumstances a single heavy electron must be able to change its rest mass in the absence or presence of particles constituting ordinary matter. Indeed, the energy loss measurements of Blackett and Wilson indicate that most particles below about 2 X 10 8 e-volts are electrons, whereas most particles above this energy there must be a large probability of a heavy electron changing or losing its identity. Now since one may assume that charge is always conserved, it follows that there are essentially only two ways in which a single heavy electron may disappear. If, for example it has a negative charge, it may collide with a proton and communicate its charge to it, the proton changing into a neutron, or it may turn an ordinary electron by changing its rest mass. In either of these two processes, a certain amount of energy is liberated and the spin and statistics to be attributed to the heavy electron depend on whether the liberation of this energy is accompained by the simultaneous liberation of some particle having a half internal spin and obeying Fermi statistics or not. Unfortunately, so far there is no experimental evidence upon this point.

scholarly journals MORSE THEORY AND THE TOPOLOGY OF CONFIGURATION SPACE

1996 ◽  
Vol 11 (05) ◽  
pp. 823-843
Author(s):  
W.D. McGLINN ◽  
L. O’RAIFEARTAIGH ◽  
S. SEN ◽  
R.D. SORKIN
Keyword(s):  
Potential Function ◽  
Configuration Space ◽  
Morse Theory ◽  
Three Dimensional ◽  
Configuration Spaces ◽  
Arbitrary Field ◽  
Two Dimensional ◽  
Point Particles ◽  
Homology Groups ◽  
Fermi Statistics

The first and second homology groups, H1 and H2, are computed for configuration spaces of framed three-dimensional point particles with annihilation included, when up to two particles and an antiparticle are present, the types of frames considered being S2 and SO(3). Whereas a recent calculation for two-dimensional particles used the Mayer–Vietoris sequence, in the present work Morse theory is used. By constructing a potential function none of whose critical indices is less than four, we find that (for coefficients in an arbitrary field K) the homology groups H1 and H2 reduce to those of the frame space, S2 or SO(3) as the case may be. In the case of SO(3) frames this result implies that H1 (with coefficients in ℤ2) is generated by the cycle corresponding to a 2π rotation of the frame. (This same cycle is homologous to the exchange loop: the spin-statistics correlation.) It also implies that H2 is trivial, which means that there does not exist a topologically nontrivial Wess–Zumino term for SO(3) frames [in contrast to the two-dimensional case, where SO(2) frames do possess such a term]. In the case of S2 frames (with coefficients in ℝ), we conclude H2=ℝ, the generator being in effect the frame space itself. This implies that for S2 frames there does exist a Wess–Zumino term, as indeed is needed for the possibility of half-integer spin and the corresponding Fermi statistics. Taken together, these results for H1 and H2 imply that our configuration space “admits spin 1/2” for either choice of frame, meaning that the spin-statistics theorem previously proved for this space is not vacuous.

Electron states and electron transport in quasi-one-dimensional molecular systems

1985 ◽  
Vol 63 (7) ◽  
pp. 1899-1903 ◽  
Author(s):  
Alexandr S. Davydov ◽  
Ivan I. Ukrainskii
Keyword(s):  
Electron Pair ◽  
Electron System ◽  
Linear Potential ◽  
Electron Wave ◽  
Electron Pairs ◽  
One Dimensional ◽  
Molecular Systems ◽  
Fermi Statistics ◽  
Causative Factors ◽  
The Many

It is shown that the concept of electron pairs may be introduced in conducting quasi-one-dimensional systems with electron delocalization such as (CH)x and the stacks of molecule-donors and acceptors of electrons TMTSF, TTT, TCNQ, etc. The introduction of pairing proves to be useful and electronic structure and electronic processes can be easily visualized. The two causative factors in the appearance of pairs in a many-electron system with repulsion are pointed out. The first one is the electron Fermi-statistics that does not allow a spatial region to be occupied by more than two electrons. The second one is the interaction of electrons with a soft lattice. The first of these factors is important at large and intermediate electron densities ρ ≥ 1, the second one dominates at [Formula: see text]. The kink-type excitation parameters in (CH)x are considered with a non-linear potential obtained in an electron-pair approach for the many-electron wave function of (CH)x.

scholarly journals Quantization of Fields in Accordance with Modular Statistics

1975 ◽  
Vol 28 (2) ◽  
pp. 115 ◽  
Author(s):  
HS Green
Keyword(s):  
Correspondence Principle ◽  
Quantum Statistics ◽  
Field Theories ◽  
Nonlinear Field ◽  
Dynamical State ◽  
Fermi Statistics ◽  
Integral Spin ◽  
New Statistics

A new generalization of quantum statistics is described, which is different from parastatistics, though it includes Fermi statistics and parafermi statistics of order two. It can be applied to the quantization of nonlinear field theories, without violating the correspondence principle. Like parastatistics, it allows the occupation of a given dynamical state by more than one particle of half-odd-integral spin. A special feature is that quark-like particles are naturally associated in modules, which have many of the characteristics of baryons and mesons. The group theoretical properties of the new statistics, and the implied classification of states, are briefly examined.

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