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Nov
16
revised Charge-conjugation of Weyl spinors
edited body
Nov
16
revised Amplitudes in renormalized perturbation theory
edited title
Nov
16
asked Charge-conjugation of Weyl spinors
Nov
16
asked Amplitudes in renormalized perturbation theory
Nov
16
revised Pre-gauge-fixed superspace action of the RNS superstring
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Nov
16
asked Pre-gauge-fixed superspace action of the RNS superstring
Oct
24
revised Renormalizability of the Polyakov Action
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Oct
24
revised Renormalizability of the Polyakov Action
added 13 characters in body
Oct
24
accepted Renormalizability of the Polyakov Action
Oct
24
answered Renormalizability of the Polyakov Action
Oct
22
answered How does one get these definitions of the energy momentum tensor?
Oct
5
comment Is the Lorentz group compact (and if not, is U(1)?)
I also think it is mis-leading to only say that Lorentz boosts are parametrized by $v\in (-c,c)$. They are, but you mustn't forget that the group law is not simply addition in $\mathbb{R}$; instead, it is given by the usual velocity addition formula in special relativity. It turns out that this group law makes $(-c,c)$ into a Lie group which is isomorphic (as Lie groups) to $(\mathbb{R},+)$ via $\mathrm{arctanh}$.
Oct
5
comment Is the Lorentz group compact (and if not, is U(1)?)
In some sense periodic identification is absolutely crucial. There are precisely two connected $1$-dimensional Lie groups: $S^1$ and $\mathbb{R}$. These two are distinguished precisely by 'periodic identification', and furthermore, $S^1$ is compact while $\mathbb{R}$ is not. Even though $[0,c]$ or $[-c,c]$ might be compact, they are not Lie groups.
Oct
1
revised Is the Lorentz group compact (and if not, is U(1)?)
edited body
Sep
30
awarded  Notable Question
Sep
27
comment Renormalizability of the Polyakov Action
@user10001 Thanks much. Do you want to write up what you said in a comment as an answer? At this point, I could write it up myself, but I feel as if it would make more sense to give you the credit for it.
Sep
23
comment Renormalizability of the Polyakov Action
@user10001 This works (in fact, with just a bit more detail, I would accept this as an answer), but there is at least one thing that worries me about this. Presumably by $1$ in $G=1+aX+(aX)^2+\cdots$, you mean $\eta _{\mu \nu}$. If this is the case, you find that the kinetic term is given by $-\frac{1}{2}\partial _\alpha Y^\mu \partial ^\alpha Y^\nu \eta _{\mu \nu}$, which means that the field $Y^0$ has the wrong sign for its kinetic term.
Sep
23
comment Quantization of Nambu–Goto action in multiples of Planck's constant?
@LubošMotl When you say ". . . the (theory defined by) the Nambu-Goto action may be quantized and and what one gets is known as string theory . . .", do you mean, in particular, that not only is the is the Nambu-Goto action equivalent to the Polyakov action at the classical level, but it is in fact equivalent to the Polyakov action even at the quantum level? Is this unique to the string ($p=1$), or is this result true for the corresponding actions for $p$-branes as well? In particular, is it true for point-particles ($p=0$)?
Sep
23
awarded  Popular Question
Sep
14
asked Renormalizability of the Polyakov Action