The Chern-Simons theory in two-space one-time dimensions is quantized on the light-front under appropriate gauge-fixing conditions using the Hamiltonian, path integral and BRST formulations.
With the Becchi-Rouet-Stora-Tyutin(BRST) quantization of gauge theory,we solve the long-standing difficult problem of the local constraint conditions,i.e.the single occupation of a slave particle per site,in the slave...With the Becchi-Rouet-Stora-Tyutin(BRST) quantization of gauge theory,we solve the long-standing difficult problem of the local constraint conditions,i.e.the single occupation of a slave particle per site,in the slave particle theory.This difficulty is actually caused by inconsistently dealing with the local Lagrange multiplier λ_(i) which ensures the constraint:in the Hamiltonian formalism of the theory,λ_(i) is time-independent and commutes with the Hamiltonian while in the Lagrangian formalism,λ_(i)(t) becomes time-dependent and plays a role of gauge field.This implies that the redundant degrees of freedom of λ_(i)(t) are introduced and must be removed by the additional constraint,the gauge fixing condition(GFC) ?_tλ_(i)(t)= 0.In literature,this GFC was missed.We add this GFC and use the BRST quantization of gauge theory for Dirac's first-class constraints in the slave particle theory.This GFC endows λ_(i)(t) with dynamics and leads to important physical results.As an example,we study the Hubbard model at half-filling and find that the spinon is gapped in the weak U and the system is indeed a conventional metal,which resolves the paradox that the weak coupling state is a superconductor in the previous slave boson mean field(MF) theory.For the t-J model,we find that the dynamic effect of λ_(i)(t) substantially suppresses the d-wave pairing gap and then the superconducting critical temperature may be lowered at least a factor of one-fifth of the MF value which is of the order of 1000 K.The renormalized T_c is then close to that in cuprates.展开更多
In this paper we will discuss Faddeev-Popov method for gauge theories with a general form of gauge symmetry in an abstract way. We will then develope a general formalism for dealing with the BRST symmetry. This formal...In this paper we will discuss Faddeev-Popov method for gauge theories with a general form of gauge symmetry in an abstract way. We will then develope a general formalism for dealing with the BRST symmetry. This formalism will make it possible to analyse the BRST symmetry for any theory.展开更多
We study the Hamiltonian, path integral and Becchi-Rouet-Stora and Tyutin (BRST) formulations of the restricted gauge theory of QCD2 à la Cho et al. under appropriate gauge-fixing conditions.
In the present work we study the Hamiltonian, path integral and BRST formulations of the Chern-Simons-Higgs theory in two-space one-time dimensions, in the so-called broken symmetry phase of the Higgs potential (where...In the present work we study the Hamiltonian, path integral and BRST formulations of the Chern-Simons-Higgs theory in two-space one-time dimensions, in the so-called broken symmetry phase of the Higgs potential (where the phase φ(xμ) of the complex matter field Φ(xμ) carries the charge degree of freedom of the complex matter field and is akin to the Goldstone boson) on the light-front (i.e., on the hyperplanes defined by the fixed light-cone time). The theory is seen to possess a set of first-class constraints and the local vector gauge symmetry. The theory being gauge-invariant is quantized under appropriate gauge-fixing conditions. The explicit Hamiltonian and path integral quantization is achieved under the above light-cone gauges. The Heisenberg equations of motion of the system are derived for the physical degrees of freedom of the system. Finally the BRST quantization of the system is achieved under appropriate BRST gauge-fixing, where the BRST symmetry is maintained even under the BRST light-cone gauge-fixing.展开更多
According to the method of path integral quantization for the canonical constrained system in Becchi-Rouet-Stora-Tyutin scheme, the supersymmetric electromagnetic interaction system was quantized. Both the Hamiltonian...According to the method of path integral quantization for the canonical constrained system in Becchi-Rouet-Stora-Tyutin scheme, the supersymmetric electromagnetic interaction system was quantized. Both the Hamiltonian of the supersymmetric electromagnetic interaction system in phase space and the quantization procedure were simplified. The BRST generator was constructed, and the BRST transforma- tions of supersymmetric fields were gotten; the effective action was calculated, and the generating functional for the Green function was achieved; also, the gauge generator was constructed, and the gauge transformation of the system was ob- tained. Finally, the Ward-Takahashi identities based on the canonical Noether theorem were calculated, and two relations between proper vertices and propaga- tors were obtained.展开更多
We investigate the new spinor field realizations of the W3 algebra, making use of the fact that the W3 algebra can be linearized by the addition of a spin-1 current. We then use these new realizations to build the nil...We investigate the new spinor field realizations of the W3 algebra, making use of the fact that the W3 algebra can be linearized by the addition of a spin-1 current. We then use these new realizations to build the nilpotent Becchi-Rouet-Stora-Tyutin charges of the spinor non-critical W3 string.展开更多
In this paper, we investigate the spinor field realizations of the W2,4 algebra, making use of the fact that the W2,4 algebra can be linearized through the addition of a spin-1 current. And then the nilpotent BRST cha...In this paper, we investigate the spinor field realizations of the W2,4 algebra, making use of the fact that the W2,4 algebra can be linearized through the addition of a spin-1 current. And then the nilpotent BRST charges of the spinor non-critical W2,4 string were built with these realizations.展开更多
In this paper we will analyse the Aharony-Bergman-Jafferis-Maldacena(ABJM) theory in N = 1 superspace formalism.We then study the quantum gauge transformations for this ABJM theory in gaugeon formalism.We will also an...In this paper we will analyse the Aharony-Bergman-Jafferis-Maldacena(ABJM) theory in N = 1 superspace formalism.We then study the quantum gauge transformations for this ABJM theory in gaugeon formalism.We will also analyse the extended BRST symmetry for this ABJM theory in gaugeon formalism and show that these BRST transformations for this theory are nilpotent and this in turn leads to the unitary evolution of the S-matrix.展开更多
At the energy regimes close to Planck scales, the usual structure of Lorentz symmetry fails to address certain fundamental issues and eventually breaks down, thus paving the way for an alternative road map. It is thus...At the energy regimes close to Planck scales, the usual structure of Lorentz symmetry fails to address certain fundamental issues and eventually breaks down, thus paving the way for an alternative road map. It is thus argued that some subgroup of proper Lorentz group could stand consistent and might possibly help us to circumvent this problem.It is this subgroup that goes by the name of Very Special Relativity(VSR). Apart from violating rotational symmetry,VSR is believed to preserve the very tenets of special relativity. The gaugeon formalism due to type-I Yokoyama and type-II Izawa are found to be invariant under BRST symmetry. In this paper, we analyze the scope of this invariance in the scheme of VSR. Furthermore, we will obtain VSR modified Lagrangian density using path integral derivation. We will explore the consistency of VSR with regard to these theories.展开更多
We present a brief review of the cohomological solutions of self-coupling interactions of the fields in the free Yang-Mills theory. All consistent interactions among the fields have been obtained using the antifield f...We present a brief review of the cohomological solutions of self-coupling interactions of the fields in the free Yang-Mills theory. All consistent interactions among the fields have been obtained using the antifield formalism through several order BRST deformations of the master equation. It is found that the coupling deformations halt exclusively at the second order, whereas higher order deformations are obstructed due to non-local interactions. The results demonstrate the BRST cohomological derivation of the interacting Yang-Mills theory.展开更多
We study the quantization of systems with local particle-ghost symmetries. The systems contain ordinary particles including gauge bosons and their counterparts obeying different statistics. The particle-ghost symmetri...We study the quantization of systems with local particle-ghost symmetries. The systems contain ordinary particles including gauge bosons and their counterparts obeying different statistics. The particle-ghost symmetries are new type of fermionic symmetries between ordinary particles and their ghost partners, different from the space-time supersymmetry and the BRST symmetry. There is a possibility that they are useful to explain phenomena of elementary particles at a more fundamental level, by extension of our systems. We show that our systems are formulated consistently or subsidiary conditions on states guarantee the unitarity of systems, as the first step towards the construction of a realistic fundamental theory.展开更多
文摘The Chern-Simons theory in two-space one-time dimensions is quantized on the light-front under appropriate gauge-fixing conditions using the Hamiltonian, path integral and BRST formulations.
文摘With the Becchi-Rouet-Stora-Tyutin(BRST) quantization of gauge theory,we solve the long-standing difficult problem of the local constraint conditions,i.e.the single occupation of a slave particle per site,in the slave particle theory.This difficulty is actually caused by inconsistently dealing with the local Lagrange multiplier λ_(i) which ensures the constraint:in the Hamiltonian formalism of the theory,λ_(i) is time-independent and commutes with the Hamiltonian while in the Lagrangian formalism,λ_(i)(t) becomes time-dependent and plays a role of gauge field.This implies that the redundant degrees of freedom of λ_(i)(t) are introduced and must be removed by the additional constraint,the gauge fixing condition(GFC) ?_tλ_(i)(t)= 0.In literature,this GFC was missed.We add this GFC and use the BRST quantization of gauge theory for Dirac's first-class constraints in the slave particle theory.This GFC endows λ_(i)(t) with dynamics and leads to important physical results.As an example,we study the Hubbard model at half-filling and find that the spinon is gapped in the weak U and the system is indeed a conventional metal,which resolves the paradox that the weak coupling state is a superconductor in the previous slave boson mean field(MF) theory.For the t-J model,we find that the dynamic effect of λ_(i)(t) substantially suppresses the d-wave pairing gap and then the superconducting critical temperature may be lowered at least a factor of one-fifth of the MF value which is of the order of 1000 K.The renormalized T_c is then close to that in cuprates.
文摘In this paper we will discuss Faddeev-Popov method for gauge theories with a general form of gauge symmetry in an abstract way. We will then develope a general formalism for dealing with the BRST symmetry. This formalism will make it possible to analyse the BRST symmetry for any theory.
文摘We study the Hamiltonian, path integral and Becchi-Rouet-Stora and Tyutin (BRST) formulations of the restricted gauge theory of QCD2 à la Cho et al. under appropriate gauge-fixing conditions.
文摘In the present work we study the Hamiltonian, path integral and BRST formulations of the Chern-Simons-Higgs theory in two-space one-time dimensions, in the so-called broken symmetry phase of the Higgs potential (where the phase φ(xμ) of the complex matter field Φ(xμ) carries the charge degree of freedom of the complex matter field and is akin to the Goldstone boson) on the light-front (i.e., on the hyperplanes defined by the fixed light-cone time). The theory is seen to possess a set of first-class constraints and the local vector gauge symmetry. The theory being gauge-invariant is quantized under appropriate gauge-fixing conditions. The explicit Hamiltonian and path integral quantization is achieved under the above light-cone gauges. The Heisenberg equations of motion of the system are derived for the physical degrees of freedom of the system. Finally the BRST quantization of the system is achieved under appropriate BRST gauge-fixing, where the BRST symmetry is maintained even under the BRST light-cone gauge-fixing.
基金Supported by Knowledge Innovation Project of the Chinese Academy of Sciences (Grant Nos. KJCX2-SW-N02 and KJCX2-SW-N016)the National Natural Science Foundation of China (Grant Nos. 10435080 and 10575123)+1 种基金Beijing Natural Science Foundation (Grant No. 1072005)the Science and Technology Development Foundation of Beijing Municipal Education Committee (Grant No. Km200310005018)
文摘According to the method of path integral quantization for the canonical constrained system in Becchi-Rouet-Stora-Tyutin scheme, the supersymmetric electromagnetic interaction system was quantized. Both the Hamiltonian of the supersymmetric electromagnetic interaction system in phase space and the quantization procedure were simplified. The BRST generator was constructed, and the BRST transforma- tions of supersymmetric fields were gotten; the effective action was calculated, and the generating functional for the Green function was achieved; also, the gauge generator was constructed, and the gauge transformation of the system was ob- tained. Finally, the Ward-Takahashi identities based on the canonical Noether theorem were calculated, and two relations between proper vertices and propaga- tors were obtained.
基金Supported by the National Natural Science Foundation of China under Grant No 10275030.
文摘We investigate the new spinor field realizations of the W3 algebra, making use of the fact that the W3 algebra can be linearized by the addition of a spin-1 current. We then use these new realizations to build the nilpotent Becchi-Rouet-Stora-Tyutin charges of the spinor non-critical W3 string.
基金The project supported by National Natural Science Foundation of China under Grant No. 10275030. It is a pleasure to thank Prof. Y.S. Duan and Dr. H. Wei for useful discussions. We have also made extensive use of a Mathematica package for calculating 0PEs, written by Prof. K. Thielemans.
文摘In this paper, we investigate the spinor field realizations of the W2,4 algebra, making use of the fact that the W2,4 algebra can be linearized through the addition of a spin-1 current. And then the nilpotent BRST charges of the spinor non-critical W2,4 string were built with these realizations.
文摘In this paper we will analyse the Aharony-Bergman-Jafferis-Maldacena(ABJM) theory in N = 1 superspace formalism.We then study the quantum gauge transformations for this ABJM theory in gaugeon formalism.We will also analyse the extended BRST symmetry for this ABJM theory in gaugeon formalism and show that these BRST transformations for this theory are nilpotent and this in turn leads to the unitary evolution of the S-matrix.
文摘At the energy regimes close to Planck scales, the usual structure of Lorentz symmetry fails to address certain fundamental issues and eventually breaks down, thus paving the way for an alternative road map. It is thus argued that some subgroup of proper Lorentz group could stand consistent and might possibly help us to circumvent this problem.It is this subgroup that goes by the name of Very Special Relativity(VSR). Apart from violating rotational symmetry,VSR is believed to preserve the very tenets of special relativity. The gaugeon formalism due to type-I Yokoyama and type-II Izawa are found to be invariant under BRST symmetry. In this paper, we analyze the scope of this invariance in the scheme of VSR. Furthermore, we will obtain VSR modified Lagrangian density using path integral derivation. We will explore the consistency of VSR with regard to these theories.
文摘We present a brief review of the cohomological solutions of self-coupling interactions of the fields in the free Yang-Mills theory. All consistent interactions among the fields have been obtained using the antifield formalism through several order BRST deformations of the master equation. It is found that the coupling deformations halt exclusively at the second order, whereas higher order deformations are obstructed due to non-local interactions. The results demonstrate the BRST cohomological derivation of the interacting Yang-Mills theory.
文摘We study the quantization of systems with local particle-ghost symmetries. The systems contain ordinary particles including gauge bosons and their counterparts obeying different statistics. The particle-ghost symmetries are new type of fermionic symmetries between ordinary particles and their ghost partners, different from the space-time supersymmetry and the BRST symmetry. There is a possibility that they are useful to explain phenomena of elementary particles at a more fundamental level, by extension of our systems. We show that our systems are formulated consistently or subsidiary conditions on states guarantee the unitarity of systems, as the first step towards the construction of a realistic fundamental theory.
