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Line 131: :<math>H_f=\int d^{d-1}x \frac{1}{2}\alpha^{-1}(\pi_\sigma,\pi_\sigma)+\frac{1}{2}\alpha(\vec{D}\sigma\cdot\vec{D}\sigma)-\frac{g^2}{2}\eta(\vec{\pi}_A,\vec{\pi}_A)-\frac{1}{2g^2}\eta(\bold{B}\cdot \bold{B})-\eta(\pi_\phi,f)-<\pi_\sigma,\phi[\sigma]>-\eta(\phi,\vec{D}\cdot\vec{\pi}_A).</math> ~~Note that the~~The last two terms are a linear combination of the Gaussian constraints and we have a whole family of (gauge equivalent)Hamiltonians parametrized by ''f''. In fact, since the last three terms vanish for the constrained states, we can drop them. ==See also== ~~See also [[Dirac bracket]], [[second class constraints]], [[BRST]], [[analysis of flows]]~~ [[Dirac bracket]], [[second class constraints]], [[BRST]], [[analysis of flows]] ==References== *{{Citation \| last1=Dirac \| first1=Paul A. M. \| title=Lectures on quantum mechanics \| url=http://books.google.com/books?id=GVwzb1rZW9kC \| publisher=Belfer Graduate School of Science, New York \| series=Belfer Graduate School of Science Monographs Series \| id={{MR\|2220894}} Reprinted by Dover in 2001. \| year=1964 \| volume=2}} {{DEFAULTSORT:First Class Constraint}}

First-class constraint: Difference between revisions