Quantum Mechanical Hamiltonians with Large Ground-State Degeneracy

Nonrelativistic Hamiltonians with large, even infinite, ground-state degeneracy are studied by connecting the degeneracy to the property of a Dirac operator. We then identify a special class of Hamiltonians, for which the full space of degenerate ground states in any spatial dimension can be exhibited explicitly. The two-dimensional version of the latter coincides with the Pauli Hamiltonian, and recently-discussed models leading to higher-dimensional Landau levels are obtained as special cases of the higher-dimensional version of this Hamiltonian. But, in our framework, it is only the asymptotic behavior of the background `potential' that matters for the ground-state degeneracy. We work out in detail the ground states of the three-dimensional model in the presence of a uniform magnetic field and such potential. In the latter case one can see degenerate stacking of all 2d Landau levels along the magnetic field axis.Comment: 14 page

Quantum Description of Anyons: Role of Contact Terms

We make an all-order analysis to establish the precise correspondence between nonrelativistic Chern-Simons quantum field theory and an appropriate first-quantized description. Physical role of the field-theoretic contact term in the context of renormalized perturbation theory is clarifed through their connection to self-adjoint extension of the Hamiltonian in the first-quantized approach. Our analysis provides a firm theoretical foundation on quantum field theories of nonrelativistic anyons.Comment: 27 pages and 7 figure

Calculation of renormalized fermion effective actions in radially symmetric non-Abelian backgrounds

Our recent method to calculate renormalized functional determinants, the partial wave cutoff method, is extended for the evaluation of 4-D fermion one-loop effective action with arbitrary mass in certain types of radially symmetric, non-Abelian, background gauge fields (including instanton-like and instanton-antiinstanton-like configurations). A detailed study on functional determinants for matrix-valued radial differential operators is presented, explicating both our analytic treatment on the high partial wave contribution and the application of the generalized Gel'fand-Yaglom formula to determine the low partial wave contribution. In general, some numerical work is needed for the low partial wave part. In the massless limit, however, the factorizable nature of our partial-wave radial differential operators can be exploited to evaluate semi-analytically even the low partial wave part, and we thus have the full fermion effective action calculated explicitly in a class of non-Abelian background gauge fields. With nonzero mass, we also perform necessary numerical analysis as regards the low partial wave contribution to produce numerically exact results for the massive effective action. Comparing these against the results of the large mass expansion, the validity range of the large mass expansion is addressed. Also studied is the fermion mass dependence of the effective instanton-antiinstanton interaction.Comment: 50pages, 11figures, revtex, fig10 replace

DIALEKTY NA GRANICY KOREAŃSKO-CHIŃSKIEJ

In this paper, we seek a closer comparative dialectological study of the dialects of the Democratic People’s Republic of Korea and the Korean dialects of the ethnically Korean Chinese near the Korea-China border. Accessible resources published in English and other languages besides Korean are particularly necessary in these times of increasing instability in the North Korean regime and foreseeable cases of asylum seekers. Speech samples are discussed to illustrate the relative difficulty of distinguishing between North Korean and Korean-Chinese speakers, compared to distinguishing between North Korean and South Korean speakers. Based on an over-view of previous literature, some guidelines are developed for identifying some distinguishing characteristics of these speech communities. Continuing dialectological research with refugees and field research making direct comparisons between these communities are necessary for further and up-to-date insight.이 연구는 북한과, 북한-중국 국경 부근에 거주하는 한국계 중국인들의 방언 비교 분석을 다룬다. 북한 정권의 불안정과 난민의 증가가 예견되는 지금, 한국어 외에도 영어 및 다른 언어로도 볼 수 있는 자료물이 시급히 필요하다. 본고는 남-북한 방언 구분보다 북한-조선족 방언 구분이 더 힘든 점을 음성 샘플 분석을 통해 보이고, 문헌 분석을 바탕으로 이 방언들의 구분되는 특징을 찾는 데 유용한 지침을 제시한다. 지속적인 새터민들과의 협력과 비교방언학 현지조사를 통해 최신 정보를 더 구축해야 할 것이다.W niniejszym artykule przedstawione zostanie badanie dialektologiczne dialektów, jakimi posługują się użytkownicy języka Demokratycznej Republiki Ludowej Korei oraz koreańskich dialektów etnicznych u Koreańczyków pochodzenia koreańsko-chińskiego na granicy koreańsko-chińskiej. Badanie tych dialektów jest obecnie niezmiernie istotne zwłaszcza w kontekście politycznym i społecznym (w zakresie osób mogących ubiegać się o azyl). Przytoczone i omówione zostają przykłady próbek mowy by zilustrować trudności w odróżnianiu osób z Korei Północnej od osób posługujących się dialektami etnicznymi koreańsko-chińskimi. Punktem wyjścia dla zobrazowania tych trudności jest uprzednie zestawienie próbek mówców północnokoreańskich i południowokoreańskich. W oparciu o dotychczasową literaturę przedmiotu, sformułowane zostają wskazówki dotyczące sposobów identyfikacji mówców należących do tych wspólnot komunikatywnych. Wskazana jest także konieczność kontynuacji badań w tym zakresie

Massive field contributions to the QCD vacuum tunneling amplitude

For the one-loop contribution to the QCD vacuum tunneling amplitude by quarks of generic mass value, we make use of a calculational scheme exploiting a large mass expansion together with a small mass expansion. The large mass expansion for the effective action is given by a series involving higher-order Seeley-DeWitt coefficients, and we carry this expansion up to order $1/(m\rho)^8$, where $m$ denotes mass of the quark and $\rho$ the instanton size parameter. For the small mass expansion, we use the known exact expression for the particle propagation functions in an instanton background and evaluate explicitly the effective action to order $(m\rho)^2$. A smooth interpolation of the results from both expansions suggests that the quark contribution to the instanton tunneling amplitude have a relatively simple $m\rho$-dependent behavior.Comment: revtex, 4figures, 33page

Instanton Determinant with Arbitrary Quark Mass: WKB Phase-shift Method and Derivative Expansion

The fermion determinant in an instanton background for a quark field of arbitrary mass is studied using the Schwinger proper-time representation with WKB scattering phase shifts for the relevant partial-wave differential operators. Previously, results have been obtained only for the extreme small and large quark mass limits, not for intermediate interpolating mass values. We show that consistent renormalization and large-mass asymptotics requires up to third-order in the WKB approximation. This procedure leads to an almost analytic answer, requiring only modest numerical approximation, and yields excellent agreement with the well-known extreme small and large mass limits. We estimate that it differs from the exact answer by no more than 6% for generic mass values. In the philosophy of the derivative expansion the same amplitude is then studied using a Heisenberg-Euler-type effective action, and the leading order approximation gives a surprisingly accurate answer for all masses.Comment: 15 pages, 3 figure