Using the Landau and symmetric gauges for the vector potential of a constant magnetic field and the quantum problem of a charged particle moving on a flat surface, we show the classical electromagnetic gauge transform...Using the Landau and symmetric gauges for the vector potential of a constant magnetic field and the quantum problem of a charged particle moving on a flat surface, we show the classical electromagnetic gauge transformation does not correspond to a one-dimensional unitary group transformation U(1) of the wave function for the quantum case. In addition, with the re-examination of the relation between the magnetic field B and its vector potential A, we found that, in order to have a consistent formulation of the dynamics of the charged particle with both expressions, we must have that B=∇×A if and only if B≠0.展开更多
A successive gauge transformation operator Tn+k for the discrete KP(dKP) hierarchy is defined,which is involved with two types of gauge transformations operators.The determinant representation of the Tn+k is establish...A successive gauge transformation operator Tn+k for the discrete KP(dKP) hierarchy is defined,which is involved with two types of gauge transformations operators.The determinant representation of the Tn+k is established and it is used to get a new τ function τ(n+k) of the dKP hierarchy from an initial τ.In this process,we introduce a generalized discrete Wronskian determinant and some useful properties of discrete difference operators.展开更多
We revisit the vital issue of gauge dependence in the scalar-induced secondary gravitational waves(SIGWs), focusing on the radiation domination(RD) and matter domination(MD) eras. The energy density spectrum is the ma...We revisit the vital issue of gauge dependence in the scalar-induced secondary gravitational waves(SIGWs), focusing on the radiation domination(RD) and matter domination(MD) eras. The energy density spectrum is the main physical observable in such induced gravitational waves. For various gauge choices, there has been a divergence in the energy density, ?GW, of SIGWs.We calculate SIGWs in diferent gauges to quantify this divergence to address the gauge-dependent problem. In our previous studies, we had found that the energy density diverges in the polynomial power of conformal time(e.g., η^(6) in uniform density gauge). We try to fix this discrepancy by adding a counter-term that removes the fictitious terms in secondary tensor perturbations. We graphically compare the calculations in various gauges and also comment on the physical origin of the observed gauge dependence.展开更多
文摘Using the Landau and symmetric gauges for the vector potential of a constant magnetic field and the quantum problem of a charged particle moving on a flat surface, we show the classical electromagnetic gauge transformation does not correspond to a one-dimensional unitary group transformation U(1) of the wave function for the quantum case. In addition, with the re-examination of the relation between the magnetic field B and its vector potential A, we found that, in order to have a consistent formulation of the dynamics of the charged particle with both expressions, we must have that B=∇×A if and only if B≠0.
基金supported by National Natural Science Foundation of China (Grant No.10671187)the Program for New Century Excellent Talents in University (Grant No.NCET-08-0515)
文摘A successive gauge transformation operator Tn+k for the discrete KP(dKP) hierarchy is defined,which is involved with two types of gauge transformations operators.The determinant representation of the Tn+k is established and it is used to get a new τ function τ(n+k) of the dKP hierarchy from an initial τ.In this process,we introduce a generalized discrete Wronskian determinant and some useful properties of discrete difference operators.
基金supported by the National Natural Science Foundation of China (Grant Nos. 12175105, 12147175, 12247170, 11575083, and 11565017)the Top-notch Academic Programs Project of Jiangsu Higher Education Institutions (TAPP)。
文摘We revisit the vital issue of gauge dependence in the scalar-induced secondary gravitational waves(SIGWs), focusing on the radiation domination(RD) and matter domination(MD) eras. The energy density spectrum is the main physical observable in such induced gravitational waves. For various gauge choices, there has been a divergence in the energy density, ?GW, of SIGWs.We calculate SIGWs in diferent gauges to quantify this divergence to address the gauge-dependent problem. In our previous studies, we had found that the energy density diverges in the polynomial power of conformal time(e.g., η^(6) in uniform density gauge). We try to fix this discrepancy by adding a counter-term that removes the fictitious terms in secondary tensor perturbations. We graphically compare the calculations in various gauges and also comment on the physical origin of the observed gauge dependence.
