Editing String field theory (section)

===Equations of motion ===
The equations of motion are given by the following equation: 
:: <math> Q_B \Psi + \Psi * \Psi  = 0 \left. \right.  \ .</math>
Because the string field <math> \Psi </math> is an infinite collection of ordinary classical fields, these equations represent an infinite collection of non-linear coupled differential equations.  There have been two approaches to finding solutions:  First, numerically, one can truncate the string field to include only fields with mass less than a fixed bound, a procedure known as "level truncation".<ref>{{cite journal | last1=Kostelecký | first1=V. Alan | last2=Samuel | first2=Stuart | title=Spontaneous breaking of Lorentz symmetry in string theory | journal=Physical Review D | publisher=American Physical Society (APS) | volume=39 | issue=2 | date=1989-01-15 | issn=0556-2821 | doi=10.1103/physrevd.39.683 | bibcode=1989PhRvD..39..683K | pages=683–685| pmid=9959689 | hdl=2022/18649 | hdl-access=free }}</ref>  This reduces the equations of motion to a finite number of coupled differential equations and has led to the discovery of many solutions.<ref>{{cite journal | last=Zwiebach | first=Barton | title=Is the String Field Big Enough? | journal=Fortschritte der Physik | publisher=Wiley | volume=49 | issue=4–6 | year=2001 | issn=0015-8208 | doi=10.1002/1521-3978(200105)49:4/6<387::aid-prop387>3.0.co;2-z | bibcode=2001ForPh..49..387Z | page=387| doi-access=free }}</ref><ref>{{cite conference | last1=Taylor | first1=Washington | last2=Zwiebach | first2=Barton | title=Strings, Branes and Extra Dimensions | chapter=D-Branes, Tachyons, and String Field Theory | publisher=World Scientific | year=2004 | isbn=978-981-238-788-2 | doi=10.1142/9789812702821_0012 | pages=641–670|arxiv=hep-th/0311017}}</ref>  Second, following the work of Martin Schnabl <ref>{{cite journal | last=Schnabl | first=Martin | title=Analytic solution for tachyon condensation in open string field theory | journal=Advances in Theoretical and Mathematical Physics | volume=10 | issue=4 | year=2006 | issn=1095-0761 | doi=10.4310/atmp.2006.v10.n4.a1 | pages=433–501|arxiv=hep-th/0511286|doi-access=free}}</ref> one can seek analytic solutions by carefully picking an ansatz which has simple behavior under star multiplication and action by the BRST operator.  This has led to solutions representing marginal deformations, the tachyon vacuum solution<ref>{{cite journal | last1=Fuchs | first1=Ehud | last2=Kroyter | first2=Michael | title=Analytical solutions of open string field theory | journal=Physics Reports | volume=502 | issue=4–5 | year=2011 | issn=0370-1573 | doi=10.1016/j.physrep.2011.01.003 | pages=89–149|arxiv=0807.4722| bibcode=2011PhR...502...89F | s2cid=119203368 }}</ref> and time-independent D-brane systems.<ref>{{cite journal | last1=Erler | first1=Theodore | last2=Maccaferri | first2=Carlo | title=String field theory solution for any open string background | journal=Journal of High Energy Physics | publisher=Springer Nature | volume=2014 | issue=10 | year=2014 | issn=1029-8479 | doi=10.1007/jhep10(2014)029 | page=029|arxiv=1406.3021| bibcode=2014JHEP...10..029E |doi-access=free}}</ref>