Variational bicomplexes

The formulation of classical field theory in terms of variational bicomplexes seems very interesting and promising. See the following references:

1. I. Anderson : The Variational Bicomplex. Very nice explanation about the basics of variational bicomplexes.

http://deferentialgeometry.org/papers/The%20Variational%20Bicomplex.pdf

2. G. Giachetta et al. : Advanced Classical Field Theory. Also includes classical BV formalism in terms of variational bicomplexes.

http://www.worldscientific.com/worldscibooks/10.1142/7189

3. L. Dickey: Soliton equations and hamiltonian systems. This is mainly about integrable hierarchies, but the last two chapters discuss the connections with variational bicomplexes.

http://www.worldscientific.com/worldscibooks/10.1142/1109

4. Also, Dubrovin - Zhang’s famous paper (book?) about higher genus Gromov - Witten invariants in terms of integrable hierarchies related to semisimple Frobenius manifolds also uses this notion.

https://arxiv.org/abs/math/0108160

Enjoy!

Ghostbusters

One of the popular movies at the moment is Ghostbusters.

Recently I had been trying to understand a few things about the ghosts and their friends myself, and inevitably arrived at Alexandrov - Kontsevich - Schwarz - Zaboronsky.

https://arxiv.org/abs/hep-th/9502010

At first I wanted to look at Pantev - Toen - Vaquie - Vezzosi since AKSZ is from pre-derived era, but now I see why AKSZ and PTVV are always mentioned together. It looks to me that AKSZ contains the essential intuition, and PTVV recasts it in derived terms.

http://arxiv.org/abs/1111.3209