- #1

- 87

- 26

## Main Question or Discussion Point

How was supersymmetry discovered? 13:00 And what were the original motivations for it? Is there some kind of intuitive way to look at and work with the formulas? For instance, in the theory of differential forms, the scalar product of two 1-forms U and V is *(U ∧ *V) = U

$$X^\mu = x^\mu + \theta \psi_+^\mu + \bar{\theta} \psi_-^\mu + \theta \bar{\theta} F$$

Can this be thought of as some kind of four component object? Or take the canonical momentum

$$\Pi_m^\mu = \partial_m x^\mu - i\bar{\theta}^I \Gamma^\mu \partial_m \theta^I$$

with action S

$$S_1[x, \theta] = \frac{1}{8\pi} \int_\Sigma g^{mn} \eta_{\mu\nu} \Pi_m^\mu \Pi_n^\nu$$

$$S_2[x, \theta] = \frac{1}{4\pi} \int_\Sigma \{ -i \ dx^\mu \wedge (\bar{\theta}^1 \Gamma_\mu d\theta^1 - \bar{\theta}^2 \Gamma_\mu d\theta^2) + \bar{\theta}^1 \Gamma_\mu d\theta^1 \wedge \bar{\theta}^2 \Gamma_\mu d\theta^2 \}$$

In the expression for ##\Pi_m^\mu##, we have two similar things ##\partial_m x^\mu## and ##\partial_m \theta^I## combined together. Can this be thought of as some kind of two-component object like

_{i}V^{i}. It is useful to think of this as being similar to the product of a complex number z and its conjugate z*, giving zz* = r^{2}. However far the analogy might go, this kind of thing certainly helps to give some vague idea of what the hodge star is doing in U ∧ *V. As far as I know, supersymmetry was discovered in a formal way, but I want to know, are there any physical motivations or helpful ways to look at the formulas? Take the superfield$$X^\mu = x^\mu + \theta \psi_+^\mu + \bar{\theta} \psi_-^\mu + \theta \bar{\theta} F$$

Can this be thought of as some kind of four component object? Or take the canonical momentum

$$\Pi_m^\mu = \partial_m x^\mu - i\bar{\theta}^I \Gamma^\mu \partial_m \theta^I$$

with action S

_{1}+ S_{2}$$S_1[x, \theta] = \frac{1}{8\pi} \int_\Sigma g^{mn} \eta_{\mu\nu} \Pi_m^\mu \Pi_n^\nu$$

$$S_2[x, \theta] = \frac{1}{4\pi} \int_\Sigma \{ -i \ dx^\mu \wedge (\bar{\theta}^1 \Gamma_\mu d\theta^1 - \bar{\theta}^2 \Gamma_\mu d\theta^2) + \bar{\theta}^1 \Gamma_\mu d\theta^1 \wedge \bar{\theta}^2 \Gamma_\mu d\theta^2 \}$$

In the expression for ##\Pi_m^\mu##, we have two similar things ##\partial_m x^\mu## and ##\partial_m \theta^I## combined together. Can this be thought of as some kind of two-component object like

*x + iy*, where the role of i is played by ##i\bar{\theta}^I \Gamma^\mu##?
Last edited: