can sum1 plz explein super springfield theory 2 me

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can sum1 plz explein super springfield theory 2 me

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>>7811236

Ok, Springfield Theory is the second quantization of Spring Theory.

Spring Theory is a proposed unified theory of physics where everything in the universe is made up of these tiny fundamental objects called springs.

We study these "springs" in terms of what is called there worldareas. To understand what a worldarea is, think of a classical spring. A spring will propagate back and forth in a sort of constrained wavelike motion. The area the spring "swipes out" as it propagates back and worth is what we call the WorldArea.

These WorldAreas are extremely convenient as they can just be viewed as 2-manifolds. In fact, due to physical symmetries, we can actually view them as Riemann Surfaces.

We parametrize the worldarea of a spring in terms of a space-like and a time-like coordinate, [math] \left( {\sigma ,\tau } \right) [/math].

We then define a metric on this worldarea [math] {h_{\alpha \beta }}\left( {\sigma ,\tau } \right) [/math].

We can now define an action of our spring theory in terms of its world area,

[math] S = \frac{1}{2}\int {{d^2}\sigma \left( {\sqrt { - h} {h^{\alpha \beta }}{g_{\mu \nu }}{\partial _\alpha }{X^\mu }{\partial _\beta }{X^\nu } - k{g_{\mu \nu }}{X^\mu }{X^\nu }} \right)} [/math].

Where [math] {g_{\mu \nu }} [/math] is the metric of the background spacetime and [math] {X^\mu }\left( {\sigma ,\tau } \right) [/math] are embeddings of the worldarea into the background spacetime.

The second quantization would be done using something like...

[math] Z = \frac{1}{{Vol}}\int\limits_{\mathcal{M}/\~} {\mathcal{D}{h_{\alpha \beta }}\mathcal{D}{X^\mu }\exp \left[ {i\frac{1}{2}\int {{d^2}\sigma \left( {\sqrt { - h} {h^{\alpha \beta }}{g_{\mu \nu }}{\partial _\alpha }{X^\mu }{\partial _\beta }{X^\nu } - k{g_{\mu \nu }}{X^\mu }{X^\nu }} \right)} } \right]} [/math]

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>>7811277

Kek

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>>7811277

2/10

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>>7811277

If this counts as shitposting, it is the classiest shitposting I have ever seen.

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