New answers tagged string-theory
5
I'm going to stick my neck out here and summarize the comment threads above as an answer of sorts. I'll delete it if it pulls down my reputation score :-/
The universe in which we happen to find ourselves is, as near as we can tell, not structured in a way that would support different values of its fundamental parameters in different locations within it- ...
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I know that a lot of time has passed, but maybe I can give my own answer to your question.
Start by slightly modifying your relation in the following way
\begin{align}
:\mathcal{F}::\mathcal{G}:= exp\left(\int d^2z_1d^2z_2\frac{1}{z_{12}}\left[\overrightarrow{\frac{\delta}{\delta b_{\mathcal{F}}(z_1)}}\overleftarrow{\frac{\delta}{\delta c_{\mathcal{G}}(z_2)}...
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Perhaps the simplest derivation that the string stiffens $X^{\prime}\to 0$ in the point particle limit with infinite string tension $T_0\to \infty$ comes from the corresponding Hamiltonian formulations:
On one hand, the Nambu-Goto Hamiltonian Lagrangian is
$$ L_H~:=~\int_0^{\ell}\! d\sigma~{\cal L}_H, \qquad {\cal L}_H ~:=~ P\cdot \dot{X}-{\cal H}, \qquad {...
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From Polchinski's String Theory, Chapter 1:
We want to study the classical and quantum dynamics of a one-dimensional object, a string. The string moves in $D$ flat spacetime dimensions, with metric $\eta_{\mu \nu} = \mathrm{diag}(-,+,+,\cdots,+)$.
So all additional dimensions are spacelike.
Strictly speaking Polchinski is only talking about bosonic ...
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Why any expectation value can be computed by this path integral, and not just the time-ordered ones?
FWIW, eq. (2.1.14) is in the Euclidean formulation, while eq. (A.1.17) is in the Minkowskian formulation. The operators inside the expectation value on the LHS of eq. (2.1.14) are implicitly assumed to be radially ordered.
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