Geometric Phase and Chiral Anomaly in Path Integral Formulation
نویسنده
چکیده
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 path integral. 1 Second quantization To analyze various geometric phases in a unified manner [1]-[8], we start with an arbitrary complete basis set
منابع مشابه
Global Anomalies in Chiral Gauge Theories on the Lattice
We discuss the issue of global anomalies in chiral gauge theories on the lattice. In Lüscher’s approach, these obstructions make it impossible to define consistently a fermionic measure for the path integral. We show that an SU(2) theory has such a global anomaly if the Weyl fermion is in the fundamental representation. The anomaly in higher representations is also discussed. We finally show th...
متن کاملGeometric phase and chiral anomaly ; their basic differences 1 Kazuo Fujikawa
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 ...
متن کاملPath Integral Evaluation of Non-Abelian Anomaly and Pauli–Villars–Gupta Regularization
When the path integral method of anomaly evaluation is applied to chiral gauge theories, two different types of gauge anomaly, i.e., the consistent form and the covariant form, appear depending on the regularization scheme for the Jacobian factor. We clarify the relation between the regularization scheme and the Pauli–Villars–Gupta (PVG) type Lagrangian level regularization. The conventional PV...
متن کاملGauge Invariant Formulation and Bosonisation of the Schwinger Model
The functional integral of the massless Schwinger model in (1 + 1) dimensions is reduced to an integral in terms of local gauge invariant quantities. It turns out that this approach leads to a natural bosonisation scheme, yielding, in particular the famous “bosonisation rule” and giving some deeper insight into the nature of the bosonisation phenomenon. As an application, the chiral anomaly is ...
متن کاملQuantum anomalies and some recent developments
Some of the developments related to quantum anomalies and path integrals during the past 10 years are briefly discussed. The covered subjects include the issues related to the local counter term in the context of 2-dimensional path integral bosonization and the treatment of chiral anomaly and index theorem on the lattice. We also briefly comment on a recent analysis of the connection between th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008