QUATERNIONIC (ALIAS Sp(2)) COHERENT STATE AND HILBERT CONNECTION

1990 ◽  
Vol 05 (22) ◽  
pp. 1765-1772 ◽  
Author(s):  
HIROSHI KURATSUJI ◽  
KENICHI TAKADA
Keyword(s):  
Euclidean Space ◽  
Coherent State ◽  
Projective Space ◽  
Gauge Field ◽  
Path Integral ◽  
Topological Invariant ◽  
Dimensional Euclidean Space ◽  
Quaternionic Projective Space ◽  
Yang Mills ◽  
State Path

The Hilbert (or quantum) connection defined via the quaternionic (or Sp(2)) coherent state is studied by using coherent state path integral. This gives a non-integrable phase associated with the Yang-Mills gauge field induced on the compactified 4-dimensional Euclidean space S4(≃ P1(H) quaternionic projective space). The topological invariant is also discussed.

The perturbative β-function in the Zumino model

2001 ◽  
Vol 79 (8) ◽  
pp. 1099-1104
Author(s):  
R Clarkson ◽  
D.G.C. McKeon
Keyword(s):  
Euclidean Space ◽  
Dimensional Euclidean Space ◽  
Supersymmetric Model ◽  
Yang Mills ◽  
Β Function ◽  
Zumino Model

We consider the perturbative β-function in a supersymmetric model in four-dimensional Euclidean space formulated by Zumino. It turns out to be equal to the β-function for N = 2 supersymmetric Yang–Mills theory despite differences that exist in the two models. PACS No.: 12.60Jv

scholarly journals A NOTE ON (SPIN-) COHERENT-STATE PATH INTEGRAL

1999 ◽  
Vol 13 (02) ◽  
pp. 107-140 ◽  
Author(s):  
JUNYA SHIBATA ◽  
SHIN TAKAGI
Keyword(s):  
Coherent State ◽  
Path Integral ◽  
Continuous Time ◽  
Classical Level ◽  
Classical Action ◽  
Single Spin ◽  
Spin Coherent State ◽  
Classical Path ◽  
Time Formalism ◽  
State Path

It is pointed out that there are some fundamental difficulties with the frequently used continuous-time formalism of the spin-coherent-state path integral. They arise already in a single-spin system and at the level of the "classical action" not to speak of fluctuations around the "classical path". Similar difficulties turn out to be present in the case of the (boson-)coherent-state path integral as well; although partially circumventable by an ingenious trick (Klauder's ∊-prescription) at the "classical level", they manifest themselves at the level of fluctuations. Detailed analysis of the origin of these difficulties makes it clear that the only way of avoiding them is to work with the proper discrete-time formalism. The thesis is explicitly illustrated with a harmonic oscillator and a spin under a constant magnetic field.

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