# Tag Info

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Julian Schwinger was a great, careful physicist. But I think it's an abuse of terminology to use the term "theory" for the collection of insights included in his "source theory". Instead, it was really a pedagogical approach to talk about quantum field theory. The pedagogical approach tried to avoid quantum fields (operator-valued functions of spacetime). ...

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I) The string (target space) coordinates $X^{\mu}(\tau_E,\sigma)$ depend on a (world sheet) spatial coordinate $\sigma$ and a (world sheet) temporal coordinate $\tau_E$ (which we here have Wick-rotated to Euclidean time, hence the subscript $E$). II) Similar to how one quantizes a field in QFT, in string theory, the Fourier series expansion of string ...

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I'll add a small disclaimer as well, I am a mathy with little to no physics background, so if any of the below needs expanding, feel free to ask! (Though I'll mention that I felt a lot more comfortable with this stuff when I first computed the induced actions I'll mention below and really got my hands dirty verifying everything.) To see that there is only ...

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The way we measure length is to use the metric tensor. Any spacetime has a metric tensor associated with it, and it's the metric tensor that is responsible for the notion of distance. To make this a little less abstract consider a concrete example. In flat spacetime the metric tensor is just: $$ds^2 = -c^2dt^2 + dx^2 + dy^2 + dx^2$$ Suppose you want to ...

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I'm not an expert on this particular topic, but I believe I can answer your question. There are different kinds of "dimensions". The standard 3 spatial dimensions we live in are infinite in extent. However, one can also imagine dimensions that have a periodicity (like a circle). In such cases, there is a "size" to the dimension that refers to the ...

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The conformal group is defined for any spacetime you want. The conformal group of d-dimensional Euclidean space, which has isometry group SO(d), is SO(d+1,1). The conformal group of d+1 dimensional Minkowski space, whose isometry group is SO(d,1), is SO(d+1,2). The defining property of the conformal group is that its the set of transformations that leave the ...

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Saying that a splitting varies over the moduli space is not completely well defined: you have to say how to identify the total spaces at different points of the moduli i.e. to specify a flat connexion on the bundle of total spaces. In the B-model, if you take the Gauss-Manin connexion as the flat connexion then the Hodge splitting varies over the moduli ...

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The solution is called Quantum Mechanics . Physics is the discipline of modeling measurements ( called data) with mathematical theories. By the nature of modeling there are limits of application. In the beginning of the modern physics era when the beautiful theories of Classical Mechanics, Thermodynamics and Electromagnetism were first proposed with ...

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It was shown by Zumino (Supersymmetry and Kahler Manifolds Phys.Lett. B87 (1979) 203 ) that the supersymmetric non-linear sigma model in four-dimensions (with target $M$) necessarily requires the manifold, $M$, to be Kahler. A dimensional reduction of this model leads to a two-dimensional nonlinear sigma model with $(2,2)$ supersymmetry. (See also: B. ...

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I don't think it's a bad question. I think as the comment says, the answer is yes, many Universes may have similar properties. However, it has been argued that our Universe's cosmological constant is finetuned, and that this fine tuning has an environmental explanation. I.e., our constant is untypical, but since observers need e.g. structure in their ...

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If the supersymetry breaking scale is close to the weak scale, the problematic renormalization parameters in the scalar sector of the Standard Model are naturally limited. In supersymemtry (when all the fields are dynamic) there are powerful non-renormalization theorems. Therefore, perturbative effects affect the scalar sector only below the supersymetry ...

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