By R. Haag

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Similar to scalars, pseudoscalars are invariant under rotations, but change sign under inversion. 22) that is, a spin component along the direction of motion. Thus, in addition to the tensor properties under transformations from the rotation group, we can classify the operators 0 by their behavior under spatial inversion p, that is, by their parity n(O), defined by the operator transformation 0 ' = POP = ±O. 1 Allowed (+) electromagnetic multipoles for quantal systems with different values of angular momenta.

57), all changes to the Lagrangian under gauge transformations canceL provided AI-' transforms as U : AI' (x) ---'> U(x)AI' (x) ut (x) + i U(x)al' U f (x). 4 Due to the non-abelian nature of QeD, gluons carry color charge and can therefore interact with each other via these vertices. 59) q where the first term describes the dynamics of quarks and their couplings to gluons, while the second term describes the dynamics of the gluon field. The strong coupling constant g is the QCD analog of the elementary electric charge e in QED.

Using this valu e of Vo in (b), the sam e function is plotted against the binding energy EB, showing that there is no other solution besides the previous one. 39) should match at r = R so that both the function u and its derivative are continuous at that point. That is also the only way to satisfy the Schrodinger equation at that point. 41) Be - kR . 42), we find K cot (KR) = -k. 43) implicitly relates the binding energy fa to the width R and depth Vo of the potential. 43) gives us a relationship between the unknown parameters Vo and R.

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Local Quantum Physics by R. Haag
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