Geometric phase and chiral anomaly ; their basic differences 1 Kazuo Fujikawa
نویسنده
چکیده
All the geometric phases are shown to be topologically trivial by using the second quantized formulation. The exact hidden local symmetry in the Schrödinger equation, which was hitherto unrecognized, controls the holonomy associated with both of the adiabatic and non-adiabatic geometric phases. The second quantized formulation is located in between the first quantized formulation and the field theory, and thus it is convenient to compare the geometric phase with the chiral anomaly in field theory. It is shown that these two notions are completely different.
منابع مشابه
J an 2 00 6 Quantum anomaly and geometric phase ; their basic differences
It is sometimes stated in the literature that the quantum anomaly is regarded as an example of the geometric phase. Though there is some superficial similarity between these two notions, we here show that the differences bewteen these two notions are more profound and fundamental. As an explicit example, we analyze in detail a quantum mechanical model proposed by M. Stone, which is supposed to ...
متن کاملGeometric Phase and Chiral Anomaly in Path Integral Formulation
All the geometric phases, adiabatic and non-adiabatic, are formulated in a unified manner in the second quantized path integral formulation. The exact hidden local symmetry inherent in the Schrödinger equation defines the holonomy. All the geometric phases are shown to be topologically trivial. The geometric phases are briefly compared to the chiral anomaly which is naturally formulated in the ...
متن کاملar X iv : h ep - t h / 05 11 14 2 v 1 1 4 N ov 2 00 5 Quantum anomaly and geometric phase ; their basic differences
It is sometimes stated in the literature that the quantum anomaly is regarded as an example of the geometric phase. Though there is some superficial similarity between these two notions, we here show that the differences bewteen these two notions are more profound and fundamental. As an explicit example, we analyze in detail a quantum mechanical model proposed by M. Stone, which is supposed to ...
متن کامل/ 94 11 06 6 v 2 1 8 M ay 1 99 5 UT - 688 , 1994 Phase Operator for the Photon Field and an Index Theorem Kazuo Fujikawa
An index relation dim ker a†a− dim ker aa† = 1 is satisfied by the creation and annihilation operators a† and a of a harmonic oscillator. A hermitian phase operator, which inevitably leads to dim ker a†a − dim ker aa† = 0, cannot be consistently defined. If one considers an s + 1 dimensional truncated theory, a hermitian phase operator of Pegg and Barnett which carries a vanishing index can be ...
متن کاملCP breaking in lattice chiral gauge theory
Discovery of gauge covariant local lattice Dirac operators [1,2], which satisfy the GinspargWilson relation [3], paved a way to a manifestly local and gauge invariant lattice formulation of anomaly-free chiral gauge theories [4]–[8]. (See also related early work in ref. [9]) It has been however pointed out that the CP symmetry, the fundamental discrete symmetry in chiral gauge theories, is not ...
متن کامل