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  • 1
    Electronic Resource
    Electronic Resource
    Topological aspects of SU(2) Weyl fermion and global anomaly (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2818-2827 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is argued here that the global anomaly of SU(2) Weyl fermions is related to the residual topological properties of massive Dirac fermions leading to the topological index corresponding to the fermion number. As in the case of the chiral anomaly with Dirac fermions, the SU(2) anomaly with a Weyl fermion vanishes when the effect of this topological property is taken into account in the Lagrangian formulation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530488
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  • 2
    Electronic Resource
    Electronic Resource
    A geometrical formulation of Abelian gauge structure in non-Abelian gauge theories and disconnected gauge group (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2270-2281 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A geometrical formalism of non-Abelian gauge theory with a topological term is constructed here with special reference to the role of Abelian gauge structures in non-Abelian theories. It is shown that when fermionic currents are written in chiral forms, we can take into account the disconnected gauge group which helps us to formulate a non-Abelian gauge structure so that the theory becomes asymptotically free.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530551
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  • 3
    Electronic Resource
    Electronic Resource
    Fractional statistics, Zp spin system, and XY model (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1090-1096 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Zp spin system in two dimensions from the point of view of fractional statistics is studied herein. It is found that, for p≤4, the system represents a gas of particles having a specific fermion number when p=2 corresponds to fermion number 1 and p=3 and 4 corresponds to a fractional fermion number. However, for p≥5, the corresponding system does not represent particles having any specific statistics; rather, it represents a hedgehog behavior. The XY model represented by a Zp spin system at p→∞ limit corresponds to bosonic kinks composed of vortex–antivortex pairs below a certain temperature. The two massive phases observed in a Zp system for 2≤p≤4 is related to their intrinsic fermionic character, and the three phases observed for p≥5 when a massless phase occurs in between two massive phases is related to the hedgehog behavior of the corresponding particles so far as their statistics is concerned. The XY model corresponding to a Zp spin system at p→∞ represents massive bosonic kinks as bound states of vortex–antivortex pairs below a certain temperature when the spin waves are massless and, as the temperature goes up, the bound states dissociate and massless kinks and massive spin waves appear. The nonexistence of an ordered phase for a continuous symmetry model is related to the inherent bosonic character of the corresponding particles.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529771
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  • 4
    Electronic Resource
    Electronic Resource
    Stochastic field theory at finite temperature and equilibrium states in quantum statistical mechanics (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 1359-1364 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Stochastic field theory at finite temperature, when it is formulated from stochastic mechanics, which incorporates Brownian motion in both the external, as well as the internal, space of a particle, and the external and internal fields, and which are written as thermal doublets, gives rise to finite temperature quantum field theory in Minkowski space. The Haag–Hugenholtz–Winnik, (HHW) formalism of modular conjugation and the Tomita–Takesaki theory of modular Hilbert algebra then follow from this finite temperature quantum field theoretical formalism. It is shown that there is an inherent discrete Z2 symmetry among the fields of the doublet, and the equilibrium condition is ensured by this symmetry. When this symmetry is spontaneously broken, thermodynamical equilibrium is destroyed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528317
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  • 5
    Electronic Resource
    Electronic Resource
    Stochastic field theory, holomorphic quantum mechanics, and supersymmetry (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 212-220 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Holomorphic quantum mechanics are studied from the point of view of stochastic quantization in Minkowski space which involves the introduction of two stochastic fields, one in the external space and the other in the internal space. The equilibrium condition is given by Z2 symmetry between the external and internal fields. In the nonequilibrium case, N=2 Wess–Zumino quantum fields are arrived at giving rise to supersymmetry. This helps to define the supercharge operator Q when the Hamiltonian is given by H=Q2 and an index theorem is derived for an interacting case when the superpotential is given by V(φ)=λφn, φ being complex with n〉2. It is found that the vacuum is degenerate and is in conformity with the result obtained by Jaffe, Lesniewski, and Lewenstein [Ann. Phys. 178, 313 (1987)] in the two-dimensional N=2 Wess–Zumino quantum field model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528863
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  • 6
    Electronic Resource
    Electronic Resource
    Gravity without metric, torsion, and topological gravity (1995)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 370-382 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The role of θ term in gravity without the metric formulation of Capovilla, Jacobson, and Dell has been investigated when the gauge group is taken to be SL(2,C) and it is shown that this corresponds to the introduction of torsion and as such represents the Einstein–Cartan action. Moreover, as this term is related to the chiral anomaly, this helps us to formulate the Einstein–Hilbert gravitational action as a symmetry-breaking effect in quantum field theory. In view of this one can consider this topological θ term as the fundamental entity. When the chiral nature of matter field is not manifested explicitly, the torsion term effectively gives rise to the cosmological constant. In case there is only the θ term in the action, one can have topological gravity which helps to realize physically Donaldson's theory of four-dimensional space–time geometry. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531312
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  • 7
    Electronic Resource
    Electronic Resource
    Topological aspects of Liouville field theory and conformal anomaly (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1178-1184 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that conformal anomaly is connected with the topological properties of the Liouville field theory which arises out of the quantum geometry necessary for the quantization procedure. As in the particle picture, the quantization of a Fermi field can be achieved through the introduction of an anisotropic feature in the internal space so that it gives rise to two internal helicities corresponding to particle and antiparticle, in case of a string, also, this specific quantum geometry gives rise to two vortex lines at the endpoints of an open string which is manifested in the Liouville field theory. This helps one to represent a Polyakov string with a nonlinear σ model with the Wess–Zumino term, and the topological aspects of this Wess–Zumino term is found to be associated with those of a Liouville field. When in the Lagrangian formulation this specific quantum geometry is taken into account, it is found that anomaly vanishes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529729
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  • 8
    Electronic Resource
    Electronic Resource
    Topological aspects of a fermion and the chiral anomaly (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 2366-2372 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is here shown that the chiral anomaly is related to the topological properties of a fermion. The quantization procedure of a relativistic particle requires that the particle be an extended one, and to quantize a Fermi field, it is necessary to introduce an anisotropic feature in the internal space of the particle so that it gives rise to two internal helicities corresponding to a particle and an antiparticle. This specific quantum geometry of a Dirac particle gives rise to the solitonic feature as envisaged by Skyrme and the Skyrme term appears as an effect of quantization. When in the Lagrangian formulation the effect of this topological property is taken into account, it is found that the anomaly vanishes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528566
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  • 9
    Electronic Resource
    Electronic Resource
    Stochastic field theory and finite-temperature supersymmetry (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1236-1240 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The finite-temperature behavior of supersymmetry is considered from the viewpoint of stochastic field theory. To this end, it is considered that Nelson's stochastic mechanics may be generalized to the quantization of a Fermi field when the classical analog of such a field is taken to be a scalar nonlocal field where the internal space is anisotropic in nature such that when quantized this gives rise to two internal helicities corresponding to fermion and antifermion. Stochastic field theory at finite temperature is then formulated from stochastic mechanics which incorporates Brownian motion in the external space as well as in the internal space of a particle. It is shown that when the anisotropy of the internal space is suppressed so that the internal time ξ0 vanishes and the internal space variables are integrated out one has supersymmetry at finite temperature. This result is true for T=0, also. However, at this phase equilibrium will be destroyed. Thus for a random process van Hove's result involving quantum mechanical operators, i.e., that when supersymmetry remains unbroken at T=0 it will also remain unbroken at T≠0, occurs. However, this formalism indicates that when at T=0 broken supersymmetry results, supersymmetry may be restored at a critical temperature Tc.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527966
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  • 10
    Electronic Resource
    Electronic Resource
    Topological aspects of a fermion, chiral anomaly, and Berry phase (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 990-997 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The relationship of the Berry phase with the topological aspects of a fermion and chiral anomaly is studied here. It is observed that this phase reflects the effect of quantum geometry when the quantization procedure of a Fermi field is considered from a classical system and may be considered as the manifestation of the multiply connected nature of quantum space-time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529752
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