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Jan
27
answered Semi-infinite forms?
Jan
20
awarded  Enlightened
Jan
20
awarded  Nice Answer
Jan
11
awarded  quantum-field-theory
Jan
10
answered Why do the conserved charges in the case of SSB of a global symmetry not exist?
Dec
15
comment How do higher-order optical chiralities look like?
Please, see the following recent review by T.G. Philibin where the conserved quantities generalizing the zilch are given in equations (21-22). These quantities correspond to the Noether symmetries given in equation (19). arxiv.org/abs/1303.0687
Dec
10
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Nov
28
awarded  Enlightened
Nov
28
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Nov
26
comment Energy in dynamical variational principle
This method is called instanton calculus. It is really not trivial to implement and requires special expertise, but it led to tremendously important discoveries in physics. The article given at the end of this note is my favorite reference doing instanton calculus on geometrical manifolds of the type obtained in the variational approach. However, it treats a much simpler problem (a single spin) than the Bose-Hubbard model. I'll try to write for you a more comprehensive answer (with more references) in the next few weeks if I can. arxiv.org/abs/cond-mat/0111139v1
Nov
26
comment Energy in dynamical variational principle
The main reason for the existence of this correction is that, while classically, all the states on the classical solution path in the trial wave function manifold are degenerate in energy, quantum mechanically there should be a unique ground state, which is obtained from quantum splitting of this degeneracy. The computation of the correction to the ground energy, indeed involves imaginary time replacement. …
Nov
26
comment Energy in dynamical variational principle
If the trial wave function manifold is close enough to the ground state, then the conserved energy value on the classical solution is a good approximation of the ground state energy. (Quantum) corrections to this first approximation can be obtained from quantizing the effective theory defined by the Lagrangian $\mathcal{L}$. Since the manifold of trial wave functions is in general non-Euclidean, one needs more general quantization techniques than canonical quantization to perform this task (e.g. geometric quantization). …
Nov
24
comment Energy in dynamical variational principle
Certainly, $E(f_n, f_n^*)$ is the Hamiltonian of the mechanical system defined by the (time independent) Lagrangian $\mathcal{L}(f_n, f_n^*, \dot{f}_n, \dot{f}_n^*)$. Thus it conserved. Please see my answer physics.stackexchange.com/questions/197297/…, where you can think of the parameter vector $R$ as the set of coefficients $f_n, f_n*$. Technically, the conservation stems from the antisymmetry of the Berry curvature.
Nov
11
revised Dirac string and Nielsen–Ninomiya theorem
added 11 characters in body
Nov
11
comment What does it mean for an action to be defined “on-shell”?
... However there are difficulties in attaining the space time supersymmetry at the quantum level. One major recent advancement in this direction is the introduction of pure spinor Green-Schwarz superstrings.
Nov
11
comment What does it mean for an action to be defined “on-shell”?
When the supersymmetry algebra does not close of-shell, then supersymmetry will not be preserved in the quantum theory. Thus even if the theory can be quantized, it would not be supersymmetric at the quantum level. The situation in supersymmetric gauge theories is even more complicated, because there are cases where the closure of the BRST algebra requires the closure of supersymmetry algebra. Strings viewed as 2 dimensional sigma models can be quantized while preserving the world sheet supersymmetry (It is not technically easy in the Neveu-Schwarz case). ...
Nov
11
answered Dirac string and Nielsen–Ninomiya theorem
Nov
5
revised What does it mean for an action to be defined “on-shell”?
edited body
Nov
5
answered What does it mean for an action to be defined “on-shell”?
Oct
31
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